A substantial fraction of workers who quit their jobs and a smaller but still substantial fraction of workers hired into jobs do not experience interim periods of unemployment (more generally, non-employment). How big the respective fractions are is difficult to say, because of the absence of good data. I summarize some of the evidence in the next section. In the U.S. where unemployment has high turnover, the average fraction of new hires coming directly from other jobs is approximately 20%. In the U.K. it might be as high as 40%. The observation of large job-to-job movements stimulated a large amount of research in search models with on-the-job search. But most of the models with on-the-job search found in the literature, although persuasive in the aras of their concentration, are still either partial or make too strong assumptions about wage determination and the demand side of the labour market (Burdett (1978), Jovanovic (1984), Mortensen, (1986)). My objective in this paper is to develop an equilibrium model of search with job-tojob movement, which is consistent with some important empirical properties of the job-to-job flow and the flow from unemployment to employment. One of the issues discussed in the paper is whether the non-cooperative search-matching model without on-the-job search, which has been extensively used in the literature to analyse unemployment flows, remains a useful tool for the analysis of unemployment and job creation. Another is whether the existence of on-the-job search adds any new insights into the behaviour of unemployment. I show that the unemployment model without on-the-job search, as discussed for example in Pissarides (1990), is robust to the introduction of on-the-job search, save for the increased complexity of the solution. The payoff is some new results, beyond the ones related to the behaviour of on-the-job search. The most interesting new results come from the fact that on-the-job search responds to the level of economic activity and relate to the dynamics of unemployment. In an examination of the evidence on the vacancy-unemployment relation in 14 OECD countries, Jackman, Pissarides and Savouri (1990) concluded that when aggregate economic activity recovered in most of these countries in the second half of the 1980s,