For quantized control, one of the powerful approaches is to use a dynamic quantizer, which has internal memories for signal quantization, with a conventional controller in the feedback control loop. The design of dynamic quantizers has become a major topic, and a number of results have been derived so far. In this paper, we extend the authors' recent result on dynamic quantizers, and applied them to a more general class of nonlinear systems, called the nonaffine nonlinear systems. Based on the performance index representing the degradation caused by the signal quantization, we propose practical dynamic quantizers, which include the authors' former result as a special case. Moreover, we provide theoretical results on the performance and on the stability of the resulting quantized systems.