This paper develops a systematic methodology for the synthesis of nonlinear multirate modelalgorithmic controllers for multivariable nonlinear systems. The control structure incorporates all available process measurements and forces each output to follow a prespecified reference trajectory regardless of the sampling period. The proposed multirate controller is a time-varying periodic system, which has properties that enable a rigorous stability analysis. Sufficient conditions for asymptotic stability of the closed-loop system are established.