Branching programs are a well established computation model for Boolean functions, especially read-once branching programs have been studied intensively.In this paper the expressive power of nondeterministic read-once branching programs, more precisely the class of functions representable in polynomial size, is investigated.For that reason two restricted models of nondeterministic read-once branching programs are defined and a lower bound method is presented.Furthermore, the first exponential lower bound for integer multiplicationon the size of a nondeterministic nonoblivious read-once branching program model is proven.