The determination of structures of multimers presents interesting new challenges. The structure(s) of the individual monomers must be found and the transformations to produce the packing interfaces must be described. A substantial difficulty results from ambiguities in assigning intermolecular distance measurements (from nuclear magnetic resonance, for example) to particular intermolecular interfaces in the structure. Here we present a rapid and efficient method to solve the packing and the assignment problems simultaneously given rigid monomer structures and (potentially ambiguous) intermolecular distance measurements. A promising application of this algorithm is to couple it with a monomer searching protocol such that each monomer structure consistent with intramolecular constraints can be subsequently input to the current algorithm to check whether it is consistent with (potentially ambiguous) intermolecular constraints. The algorithm AmbiPack uses a hierarchical division of the search space and the branch-and-bound algorithm to eliminate infeasible regions of the space. Local search methods are then focused on the remaining space. The algorithm generally runs faster as more constraints are included because more regions of the search space can be eliminated. This is not the case for other methods, for which additional constraints increase the complexity of the search space. The algorithm presented is guaranteed to find all solutions to a predetermined resolution. This resolution can be chosen arbitrarily to produce outputs at various level of detail. Illustrative applications are presented for the P22 tailspike protein (a trimer) and portions of -amyloid (an ordered aggregate). Proteins 32:26-42, 1998.