diff --git a/gensim/models/atmodel.py b/gensim/models/atmodel.py
index 838c7634e3..b0720c2f19 100755
--- a/gensim/models/atmodel.py
+++ b/gensim/models/atmodel.py
@@ -213,7 +213,8 @@ def __init__(self, corpus=None, num_topics=100, id2word=None, author2doc=None, d
                 * 'symmetric': (default) Uses a fixed symmetric prior of `1.0 / num_topics`,
                 * 'auto': Learns an asymmetric prior from the corpus.
         update_every : int, optional
-            Make updates in topic probability for latest mini-batch.
+            Number of chunks to be iterated through before each M step of EM.
+            Set to 0 for batch learning, > 1 for online iterative learning.
         eval_every : int, optional
             Calculate and estimate log perplexity for latest mini-batch.
         gamma_threshold : float, optional
@@ -803,7 +804,7 @@ def update(self, corpus=None, author2doc=None, doc2author=None, chunksize=None,
         self.state.numdocs += lencorpus
 
         if update_every:
-            updatetype = "online"
+            updatetype = "online (single-pass)" if self.passes == 1 else "online (multi-pass)"
             updateafter = min(lencorpus, update_every * self.numworkers * chunksize)
         else:
             updatetype = "batch"
diff --git a/gensim/models/ldamodel.py b/gensim/models/ldamodel.py
index 6691ddcc31..ac0d0691a1 100755
--- a/gensim/models/ldamodel.py
+++ b/gensim/models/ldamodel.py
@@ -374,7 +374,7 @@ def __init__(self, corpus=None, num_topics=100, id2word=None,
         passes : int, optional
             Number of passes through the corpus during training.
         update_every : int, optional
-            Number of documents to be iterated through for each update.
+            Number of chunks to be iterated through before each M step of EM.
             Set to 0 for batch learning, > 1 for online iterative learning.
         alpha : {float, numpy.ndarray of float, list of float, str}, optional
             A-priori belief on document-topic distribution, this can be:
@@ -932,11 +932,7 @@ def update(self, corpus, chunksize=None, decay=None, offset=None,
         self.state.numdocs += lencorpus
 
         if update_every:
-            updatetype = "online"
-            if passes == 1:
-                updatetype += " (single-pass)"
-            else:
-                updatetype += " (multi-pass)"
+            updatetype = "online (single-pass)" if self.passes == 1 else "online (multi-pass)"
             updateafter = min(lencorpus, update_every * self.numworkers * chunksize)
         else:
             updatetype = "batch"
@@ -1053,7 +1049,7 @@ def do_mstep(self, rho, other, extra_pass=False):
         ----------
         rho : float
             Learning rate.
-        other : :class:`~gensim.models.ldamodel.LdaModel`
+        other : :class:`~gensim.models.ldamodel.LdaState`
             The model whose sufficient statistics will be used to update the topics.
         extra_pass : bool, optional
             Whether this step required an additional pass over the corpus.
diff --git a/gensim/models/ldamulticore.py b/gensim/models/ldamulticore.py
index fdb5ce70a9..4171bfb35b 100644
--- a/gensim/models/ldamulticore.py
+++ b/gensim/models/ldamulticore.py
@@ -107,7 +107,7 @@ class LdaMulticore(LdaModel):
 
     """
     def __init__(self, corpus=None, num_topics=100, id2word=None, workers=None,
-                 chunksize=2000, passes=1, batch=False, alpha='symmetric',
+                 chunksize=2000, passes=1, update_every=1, alpha='symmetric',
                  eta=None, decay=0.5, offset=1.0, eval_every=10, iterations=50,
                  gamma_threshold=0.001, random_state=None, minimum_probability=0.01,
                  minimum_phi_value=0.01, per_word_topics=False, dtype=np.float32):
@@ -133,6 +133,9 @@ def __init__(self, corpus=None, num_topics=100, id2word=None, workers=None,
             Number of documents to be used in each training chunk.
         passes : int, optional
             Number of passes through the corpus during training.
+        update_every : int, optional
+            Number of chunks to be iterated through before each M step of EM.
+            Set to 0 for batch learning, > 1 for online iterative learning.
         alpha : {float, numpy.ndarray of float, list of float, str}, optional
             A-priori belief on document-topic distribution, this can be:
                 * scalar for a symmetric prior over document-topic distribution,
@@ -178,24 +181,20 @@ def __init__(self, corpus=None, num_topics=100, id2word=None, workers=None,
 
         """
         self.workers = max(1, cpu_count() - 1) if workers is None else workers
-        self.batch = batch
 
         if isinstance(alpha, str) and alpha == 'auto':
             raise NotImplementedError("auto-tuning alpha not implemented in LdaMulticore; use plain LdaModel.")
 
         super(LdaMulticore, self).__init__(
-            corpus=corpus, num_topics=num_topics,
-            id2word=id2word, chunksize=chunksize, passes=passes, alpha=alpha, eta=eta,
+            corpus=corpus, num_topics=num_topics, id2word=id2word, distributed=False,  # not distributed across machines
+            chunksize=chunksize, passes=passes, update_every=update_every, alpha=alpha, eta=eta,
             decay=decay, offset=offset, eval_every=eval_every, iterations=iterations,
-            gamma_threshold=gamma_threshold, random_state=random_state, minimum_probability=minimum_probability,
+            gamma_threshold=gamma_threshold, minimum_probability=minimum_probability, random_state=random_state,
             minimum_phi_value=minimum_phi_value, per_word_topics=per_word_topics, dtype=dtype,
         )
 
     def update(self, corpus, chunks_as_numpy=False):
-        """Train the model with new documents, by EM-iterating over `corpus` until the topics converge
-        (or until the maximum number of allowed iterations is reached).
-
-        Train the model with new documents, by EM-iterating over the corpus until the topics converge, or until
+        """Train the model with new documents, by EM-iterating over the corpus until the topics converge, or until
         the maximum number of allowed iterations is reached. `corpus` must be an iterable. The E step is distributed
         into the several processes.
 
@@ -231,14 +230,16 @@ def update(self, corpus, chunks_as_numpy=False):
 
         self.state.numdocs += lencorpus
 
-        if self.batch:
+        # Same as in LdaModel but self.workers (processes) is used instead of self.numworkers (machines)
+        if self.update_every:
+            updatetype = "online (single-pass)" if self.passes == 1 else "online (multi-pass)"
+            updateafter = min(lencorpus, self.update_every * self.workers * self.chunksize)
+        else:
             updatetype = "batch"
             updateafter = lencorpus
-        else:
-            updatetype = "online"
-            updateafter = self.chunksize * self.workers
+
         eval_every = self.eval_every or 0
-        evalafter = min(lencorpus, eval_every * updateafter)
+        evalafter = min(lencorpus, eval_every * self.workers * self.chunksize)
 
         updates_per_pass = max(1, lencorpus / updateafter)
         logger.info(