We present adaptive output-feedback schemes for a class of discrete-time systems whose continuous time counterparts are the output-feedback canonical form. We first develop a systematic design procedure for the deterministic ease, Global boundedness and convergence are achieved with no restriction imposed on the nonlinearities. Then we proceed to develop an analogous design procedure for the adaptive case. Depending on the characteristics of the nonlinearities, global boundedness and convergence can be achieved with various update laws. A rank condition is required to ensure such properties for nonlinearities which are not globally Lipchitz.