An analysis of Li-intercalation and deintercalation in a tungsten-oxide based electrochromic device is presented. An hysteresis between intercalation and deintercalation has been separately observed in both the built-in potential and the optical efficiency of the devices. This hysteresis is explained by a two-phase model in which intercalation occurs as the parallel, equipotential filling of the two phases, but where a deintercalation barrier associated with one of the phases imposes the observed asymmetry. An equivalent circuit model is given, allowing for the prediction of the deintercalation behavior from the intercalation behavior with a single adjustable parameter (representing the deintercalation barrier). The observed data are well-explained by the circuit model; using a single adjustable parameter, an accurate description of the deintercalation behavior may be obtained from the data on intercalation.