In this article, an adaptive control method-adaptive generalized generic model control (AGGMC) is proposed for a class of nonlinear time-varying processes by use of a modified strong tracking filter (MSTF). It inherits all of the advantages of generic model control (GMC) and extends GMC to nonlinear time-varying processes with relative orders larger than ones. Sufficient conditions under which the MSTF is asymptotically convergent are first derived, then, with these conditions, the resultant closedloop system under the AGGMC is proved to be Lyapunov stable. Finally, simulation studies are provided to validate the effectiveness of the proposed approach.