-The binary input JV-user adder channel models a communication media accessed simultaneously by N users. Each user transmits a binary codeword of length n chosen from its codebook and the channel output consists of a componentwise arithmetic sum of the binary digits. Van Tilborg  gave an upper bound on the size of a uniquely decodable code for the two-user case. His work is generalized here to the Nuser case. The results give interesting information on the existence and properties of such codes. Index Terms-JV-user adder channel, uniquely decodable codes.