This paper presents a simple direct adaptive control strategy for the operation of chemical processes. An efficient and easy-to-implement learning algorithm is proposed that enables a three-parameter, nonlinear controller to control the dynamic process in an adaptive and autonomous way by simply using process output errors. To guarantee the convergence of the proposed algorithm and the stability of the resultant control system, a rigorous analysis utilizing the Lyapunov approach is provided. The proposed scheme is shown to be more superior in both performance and stability than an adaptive proportional-integral-derivative algorithm, especially in handling large time-delay and higher order systems. With its advantage of a learning capability, the direct adaptive control scheme is further extended to one that is able to handle nonminimum-phase process systems directly. The key of the extension is to incorporate a minimum-phase predictor for generating a compensation signal. With the help of the predictor, the signal feeding back to the controller is, therefore, a compensated one without the undesired inverse response characteristics. Two illustrative examples are provided to demonstrate the effectiveness and applicability of the scheme for the operation of process systems in the presence of inverse response. Moreover, extensive comparisons with the well-known internal model control strategy are also included as a rigorous base for evaluating the proposed direct adaptive control scheme in handling nonminimum-phase process systems.