Physical mechanisms responsible for nonlinear phenomena and anomalous transient response of cooled extrinsic far-infrared photoconductors are discussed. A simple model describing carrier generation, trapping, and impact ionization is presented, which describes the transient response on fast time scales 10-3 to 10-4 sec, neglecting changes in space charge. Carrier heating by a dc electric field produces relatively fast, damped oscillatory response to external excitation. A small-signal analysis of these equations is a test of stability. An analysis of the role of ideal electrical contacts and space charge is also presented. The very slow (∼1 sec) overshoot and transient response commonly observed in cooled extrinsic photoconductors is explained by the dynamics of trapped space charge near the injecting electrical contact. A small-signal analysis determines the characteristic time constants for these processes, which are typically ∼1 sec. Calculated examples of the recombination and ionization coefficients, dc I-V curves, differential equation flow diagrams, and transient response are presented for parameters typical of p-type Ge photoconductors doped with shallow acceptor levels, and suggestions for the design of more stable photoconductors are presented.