A high efficiency, multi-stage fuel cell system method and apparatus is provided. The fuel cell system is comprised of multiple fuel cell stages, whereby the temperatures of the fuel and oxidant gas streams and the percentage of fuel consumed in each stage are controlled to optimize fuel cell system efficiency. The stages are connected in a serial, flow-through arrangement such that the oxidant gas and fuel gas flowing through an upstream stage is conducted directly into the next adjacent downstream stage. The fuel cell stages are further arranged such that unspent fuel and oxidant laden gases too hot to continue within an upstream stage because of material constraints are conducted into a subsequent downstream stage which comprises a similar cell configuration, however, which is constructed from materials having a higher heat tolerance and designed to meet higher thermal demands. In addition, fuel is underutilized in each stage, resulting in a higher overall fuel cell system efficiency.