Various versions of the file allocation problem on homogeneous two-level local multiaccess networks are examined. The problems associated with file allocation are more simple on two-level networks than on general point-to-point networks because the communication cost for accessing a file is reduced to a three-value variable. File allocation with storage-limit constraints is still NP-hard. The optimal solution, given these conditions, involves transformation into a pure zero-one integer programming problem and a search algorithm based on E. Balas's additive algorithm (1965). In the case in which the system is dominated by the communication cost, the simple file allocation problem is polynomially solvable. An efficient heuristic algorithm with guaranteed performance is proposed for this special case.>