  We begin a systematic study of the enumerative combinatorics of mixed
succession rules, which are succession rules such that, in the associated
generating tree, the nodes are allowed to produce their sons at several
different levels according to different production rules. Here we deal with a
specific case, namely that of two different production rules whose rule
operators commute. In this situation, we are able to give a general formula
expressing the sequence associated with the mixed succession rules in terms of
the sequences associated with the component production rules. We end by
providing some examples illustrating our approach.
