Restricted branching programs are considered in complexity theory in
order to study the space complexity of sequential computations and
in applications as a data structure for Boolean functions. In this
paper (\oplus,k)-branching programs and (\vee,k)-branching
programs are considered, i.e., branching programs starting with a
\oplus- (or \vee-)node with a fan-out of k whose successors
are k read-once branching programs. This model is motivated by the
investigation of the power of nondeterminism in branching programs
and of similar variants that have been considered as a data
structure. Lower bound methods and hierarchy results
for polynomial size (\oplus,k)- and (\vee,k)-branching programs
with respect to k are presented.