Adaptive modulation and coding (AMC) scheme is widely used in wireless and mobile communications systems supporting high-speed Internet services. A system using AMC can be modeled as that with time-varying capacity. In this paper, we propose a generalized framework of packet scheduler for wireless systems with time-varying capacity. First, we develop the fundamental scheduling algorithm (FSA) that maximizes the system throughput under given constraints by using the dual optimization technique. Even though FSA can be used as a stand-alone scheduler supporting only nonreal-time traffic, it mainly plays a role in this paper as a basic building block of the advanced scheduling algorithm (ASA). We design ASA so that it supports real-time and nonreal-time traffic simultaneously. Since ASA operates on the basis of connections, we also suggest a connection admission control algorithm that matches well with the proposed scheduler. Finally, we show an application example of the proposed scheduling algorithm to the time-division multiple access system using AMC