diff --git a/doc/src/read_data.txt b/doc/src/read_data.txt
index 4ea60163b2214c35c0328975f33c97664c19635d..fd297e36c121e1efb8f631c95c182a51587a60c0 100644
--- a/doc/src/read_data.txt
+++ b/doc/src/read_data.txt
@@ -15,10 +15,11 @@ read_data file keyword args ... :pre
 file = name of data file to read in :ulb,l
 zero or more keyword/arg pairs may be appended :l
 keyword = {add} or {offset} or {shift} or {extra/atom/types} or {extra/bond/types} or {extra/angle/types} or {extra/dihedral/types} or {extra/improper/types} or {extra/bond/per/atom} or {extra/angle/per/atom} or {extra/dihedral/per/atom} or {extra/improper/per/atom} or {group} or {nocoeff} or {fix} :l
-  {add} arg = {append} or {Nstart} or {merge}
-    append = add new atoms with IDs appended to current IDs
-    Nstart = add new atoms with IDs starting with Nstart
-    merge = add new atoms with their IDs unchanged
+  {add} arg = {append} or {IDoffset} or {IDoffset MOLoffset} or {merge}
+    append = add new atoms with atom IDs appended to current IDs
+    IDoffset = add new atoms with atom IDs having IDoffset added
+    MOLoffset = add new atoms with molecule IDs having MOLoffset added (only when molecule IDs are enabled)
+    merge = add new atoms with their atom IDs (and molecule IDs) unchanged
   {offset} args = toff boff aoff doff ioff
     toff = offset to add to atom types
     boff = offset to add to bond types
@@ -120,20 +121,26 @@ boundary, then the atoms may become far apart if the box size grows.
 This will separate the atoms in the bond, which can lead to "lost"
 bond atoms or bad dynamics.
 
-The three choices for the {add} argument affect how the IDs of atoms
-in the data file are treated.  If {append} is specified, atoms in the
-data file are added to the current system, with their atom IDs reset
-so that an atomID = M in the data file becomes atomID = N+M, where N
-is the largest atom ID in the current system.  This rule is applied to
-all occurrences of atom IDs in the data file, e.g. in the Velocity or
-Bonds section.  If {Nstart} is specified, then {Nstart} is a numeric
-value is given, e.g. 1000, so that an atomID = M in the data file
-becomes atomID = 1000+M.  If {merge} is specified, the data file atoms
+The three choices for the {add} argument affect how the atom IDs and
+molecule IDs of atoms in the data file are treated.  If {append} is
+specified, atoms in the data file are added to the current system,
+with their atom IDs reset so that an atomID = M in the data file
+becomes atomID = N+M, where N is the largest atom ID in the current
+system.  This rule is applied to all occurrences of atom IDs in the
+data file, e.g. in the Velocity or Bonds section. This is also done
+for molecule IDs, if the atom style does support molecule IDs or
+they are enabled via fix property/atom. If {IDoffset} is specified,
+then {IDoffset} is a numeric value is given, e.g. 1000, so that an
+atomID = M in the data file becomes atomID = 1000+M. For systems
+with enabled molecule IDs, another numerical argument {MOLoffset}
+is required representing the equivalent offset for molecule IDs.
+If {merge} is specified, the data file atoms
 are added to the current system without changing their IDs.  They are
 assumed to merge (without duplication) with the currently defined
 atoms.  It is up to you to insure there are no multiply defined atom
 IDs, as LAMMPS only performs an incomplete check that this is the case
-by insuring the resulting max atomID >= the number of atoms.
+by insuring the resulting max atomID >= the number of atoms. For
+molecule IDs, there is no check done at all.
 
 The {offset} and {shift} keywords can only be used if the {add}
 keyword is also specified.
diff --git a/src/atom.cpp b/src/atom.cpp
index 3fa470efd5167450111f932618debfa596753321..fa86046d239be4dc9d52d4717b86130df3e12fb0 100644
--- a/src/atom.cpp
+++ b/src/atom.cpp
@@ -822,8 +822,8 @@ void Atom::deallocate_topology()
    call style-specific routine to parse line
 ------------------------------------------------------------------------- */
 
-void Atom::data_atoms(int n, char *buf, tagint id_offset, int type_offset,
-                      int shiftflag, double *shift)
+void Atom::data_atoms(int n, char *buf, tagint id_offset, tagint mol_offset,
+                      int type_offset, int shiftflag, double *shift)
 {
   int m,xptr,iptr;
   imageint imagedata;
@@ -948,6 +948,7 @@ void Atom::data_atoms(int n, char *buf, tagint id_offset, int type_offset,
         coord[2] >= sublo[2] && coord[2] < subhi[2]) {
       avec->data_atom(xdata,imagedata,values);
       if (id_offset) tag[nlocal-1] += id_offset;
+      if (mol_offset) molecule[nlocal-1] += mol_offset;
       if (type_offset) {
         type[nlocal-1] += type_offset;
         if (type[nlocal-1] > ntypes)
diff --git a/src/atom.h b/src/atom.h
index 007142a1c045f90f24981b1facbf92e3c10cc20b..62c2d64ca7dfdd574172c3440b5b6109023574a6 100644
--- a/src/atom.h
+++ b/src/atom.h
@@ -229,7 +229,7 @@ class Atom : protected Pointers {
 
   void deallocate_topology();
 
-  void data_atoms(int, char *, tagint, int, int, double *);
+  void data_atoms(int, char *, tagint, tagint, int, int, double *);
   void data_vels(int, char *, tagint);
   void data_bonds(int, char *, int *, tagint, int);
   void data_angles(int, char *, int *, tagint, int);
diff --git a/src/read_data.cpp b/src/read_data.cpp
index b1a42608c050a1214fb3eed63df2f19554159e1c..3b93098a6e7bdedfcb874c7926be5ef4cba3b62d 100644
--- a/src/read_data.cpp
+++ b/src/read_data.cpp
@@ -124,7 +124,7 @@ void ReadData::command(int narg, char **arg)
 
   addflag = NONE;
   coeffflag = 1;
-  id_offset = 0;
+  id_offset = mol_offset = 0;
   offsetflag = shiftflag = 0;
   toffset = boffset = aoffset = doffset = ioffset = 0;
   shift[0] = shift[1] = shift[2] = 0.0;
@@ -145,11 +145,21 @@ void ReadData::command(int narg, char **arg)
       if (strcmp(arg[iarg+1],"append") == 0) addflag = APPEND;
       else if (strcmp(arg[iarg+1],"merge") == 0) addflag = MERGE;
       else {
+        if (atom->molecule_flag && (iarg+3 > narg))
+          error->all(FLERR,"Illegal read_data command");
         addflag = VALUE;
         bigint offset = force->bnumeric(FLERR,arg[iarg+1]);
         if (offset > MAXTAGINT)
-          error->all(FLERR,"Read data add offset is too big");
+          error->all(FLERR,"Read data add atomID offset is too big");
         id_offset = offset;
+
+        if (atom->molecule_flag) {
+          offset = force->bnumeric(FLERR,arg[iarg+2]);
+          if (offset > MAXTAGINT)
+            error->all(FLERR,"Read data add molID offset is too big");
+          mol_offset = offset;
+          iarg++;
+        }
       }
       iarg += 2;
     } else if (strcmp(arg[iarg],"offset") == 0) {
@@ -310,14 +320,18 @@ void ReadData::command(int narg, char **arg)
     update->ntimestep = 0;
   }
 
-  // compute atomID offset for addflag = MERGE
+  // compute atomID and optionally moleculeID offset for addflag = APPEND
 
   if (addflag == APPEND) {
     tagint *tag = atom->tag;
+    tagint *molecule = atom->molecule;
     int nlocal = atom->nlocal;
-    tagint max = 0;
-    for (int i = 0; i < nlocal; i++) max = MAX(max,tag[i]);
-    MPI_Allreduce(&max,&id_offset,1,MPI_LMP_TAGINT,MPI_MAX,world);
+    tagint maxid = 0, maxmol = 0;
+    for (int i = 0; i < nlocal; i++) maxid = MAX(maxid,tag[i]);
+    if (atom->molecule_flag)
+      for (int i = 0; i < nlocal; i++) maxmol = MAX(maxmol,molecule[i]);
+    MPI_Allreduce(&maxid,&id_offset,1,MPI_LMP_TAGINT,MPI_MAX,world);
+    MPI_Allreduce(&maxmol,&mol_offset,1,MPI_LMP_TAGINT,MPI_MAX,world);
   }
 
   // set up pointer to hold original styles while we replace them with "zero"
@@ -1137,7 +1151,7 @@ void ReadData::atoms()
     nchunk = MIN(natoms-nread,CHUNK);
     eof = comm->read_lines_from_file(fp,nchunk,MAXLINE,buffer);
     if (eof) error->all(FLERR,"Unexpected end of data file");
-    atom->data_atoms(nchunk,buffer,id_offset,toffset,shiftflag,shift);
+    atom->data_atoms(nchunk,buffer,id_offset,mol_offset,toffset,shiftflag,shift);
     nread += nchunk;
   }
 
diff --git a/src/read_data.h b/src/read_data.h
index 730229c72296fccdfc86ec401051801f6bd6ae27..b85ed67dcdc1d96eb308cfa8710941fcfb7456d4 100644
--- a/src/read_data.h
+++ b/src/read_data.h
@@ -39,7 +39,7 @@ class ReadData : protected Pointers {
   int narg,maxarg;
   char argoffset1[8],argoffset2[8];
 
-  bigint id_offset;
+  bigint id_offset, mol_offset;
 
   int nlocal_previous;
   bigint natoms;