ABSTRACT. We consider the problem of unification modulo an equational theory ACh, which consists of a function h which is homomorphic over an associative-commutative operator +. Unification modulo ACh is undecidable, so we define a bounded ACh unification problem. In this bounded version of ACh unification we essentially bound the number of times h can be recursively applied to a term, and only allow solutions that satisfy this bound. There is no bound on the number of occurrences of h in a term, and the + symbol can be applied an unlimited number of times. We give inference rules for solving bounded ACh unification, and we prove that the rules are sound, complete and terminating. We have implemented the algorithm in Maude and give experimental results. We argue that this algorithm is useful in cryptographic protocol analysis.