In this paper, effective capacity of a two-way amplify and forward (AF) relay channel, in which two source nodes exchange their signals via a relay node, is analyzed. Depending on the availability of the channel side information (CSI), the relay, which operates in half-duplex mode, has a fixed-gain or variable-gain factor. It is assumed that source nodes are subject to individual statistical quality of service (QoS) constraints in the form of limitations on buffer size. Under these assumptions and constraints, a characterization of the throughput for source nodes is provided by obtaining closed-form expressions for lower bounds on the effective capacity. Performances of two-way fixed-gain and variable-gain AF relaying are compared. The relations between buffer constraints, transmission power, the location of the relay node and effective capacity are also studied.