This paper proposes a novel model-based direct adaptive control (DAC) strategy for a class of nonlinear processes whose nominal model is input-output linearizable but may not be accurate enough to represent the actual process. The proposed DAC scheme is composed of two parts: the first is a model based part that makes use of the available process model for a nominal performance, and the second is an adaptive, nonlinear shape-tunable controller (STC) that is used to compensate for the model errors. To update the STC's shape parameters such that the modeling errors can be accommodated adaptively, a simple and effective parameter tuning algorithm is devised. The offset-free control performance and the stability of the resultant nonlinear control system are guaranteed by a Lyapunov-based approach, which involves two distinctive performance indices to relate, respectively, the process output error and a specially designed auxiliary signal. Furthermore, by simply manipulating the output range of the STC, the proposed DAC scheme is further extended to one that is able to handle nonlinear processes in the presence of hard input constraints. The effectiveness and applicability of the proposed DAC control scheme were examined through the regulatory control of a nonlinear, continuous stirred-tank reactor and the temperature trajectory tracking control of an input-constrained batch reactor under the influence of diversified process disturbances. Simulation results reveal that the proposed model-based DAC scheme is superior to a model-based linearizing control strategy, a sliding mode controller, and an intelligent, model-free DAC scheme, especially when faced with significant plant/model mismatch and unanticipated uncertainties.