Two-dimensional transient analysis of field-plate AlGaN/GaN HEMTs and GaN MESFETs is performed, considering a deep donor and a deep acceptor in the semi-insulating GaN buffer layer. Quasi-pulsed I-V curves are derived from the transient characteristics. It is studied how the existence of a field plate affects buffer-related drain lag, gate lag and current collapse. It is shown that in both FETs, the drain lag is reduced by introducing a field plate, because electron injection into the buffer layer is weakened by it, and trapping effects are reduced. It is also shown that the buffer-related current collapse and gate lag are reduced in the field-plate structures. The dependence on SiN passivation layer thickness under the field plate is also studied, suggesting that there is an optimum thickness of the SiN layer to minimize buffer-related current collapse and drain lag in GaN HEMTs and MESFETs.