Generally, structural job search models are taken to be stationary. In this paper models are examined in which every exogenous variable can cause nonstationarity, for instance because its value is dependent on unemployment duration. A general differential equation that describes the evolution of the reservation wage over time is derived. As an empirical illustration a nonstationary structural model is estimated that focuses on the consequences of a downward shift in the level of benefits. It appears that the elasticity of duration with respect to the level of benefits after the shift is much larger than the elasticity with respect to the level before the shift. This paper examines the movement of a job-seeking individual's reservation wage over time in a general nonstationary job search model. Also, results concerning comparative dynamics of the reservation wage and the distribution of the duration of unemployment are derived. As an empirical illustration a nonstationary structural model is estimated. The nonstationarity originates from the decrease in the level of benefits when unemployment duration equals two years. From the results some detailed policy recommendations can be deduced, as one is able to distinguish the effect of a change in the level of benefits in the first two years of unemployment from the effect of a change in the level after that period. Recently the use of job search models for the analysis of unemployment duration has become widespread. The reduced-form approach in empirical studies (see e.g. Lancaster (1979)), in which only the hazard of the duration distribution is estimated, is gradually being replaced by a more structural approach. The latter way of modelling is characterized by the explicit use in empirical analysis of the reservation wage equation as stated by the theory. E.g. Yoon (1981), Lancaster and Chesher (1983), Lynch (1983), Narendranathan and Nickell (1985) and van den Berg (1988) use the complete theoretical framework of job search theory to make inferences about search behaviour. However, the structural models used in these studies are stationary. This implies that variables like unemployment benefits or the rate of arrival of job offers are assumed to be constant over the spell of unemployment, which is often at variance with reality. What is more, various reduced-form empirical studies indicate a significant durationdependence of the re-employment probability, which is generally interpreted as evidence in favour of the presence of nonstationarity (see e.g. Blau and Robins (1986), Kooreman and Ridder (1983), Lancaster (1979) and Narendranathan, Nickell and Stern (1985)). Consequently there is a need to model reservation wage movements over time based on a nonstationary theoretical framework.