There is now a voluminous, and rapidly expanding, literature on the economics of job search. Throughout this extensive literature there are two basic underlying assumptions. First, the process of indulging in search (that is, of obtaining job offers) is assumed to be costly. This is the case whether the model is concerned with off-the-job search (that is, search by unemployed workers) or with on-the-job search (that is, search by employed workers). Second, and in contrast, the actual process of changing jobs (or of changing from being unemployed to being employed, or vice versa) is assumed to be costless. For some occupations, this pair of assumptions may well be realistic. However, there appears to be a wide variety of occupations in which the reverse of these two assumptions is more likely to be the case: namely, that actual search is relatively costless, but that the process of changing occupational states is relatively costly. A good example is provided by university teachers. For them, the cost of search is virtually zero; it consists of scanning certain quality newspapers once a week (which, being lively-minded potentially top people, they would be doing anyhow), submitting a curriculum vitae when an appropriate job appears, and then attending (if fortunate) an expenses-paid interview. On the other hand, the process of changing jobs can be very costly; usually it will involve moving to another town, which will necessitate expenditure on buying and selling houses, of furniture (though this may be partially refunded by the new employer), and redecoration of the new home. Moreover, considerable psychic costs are incurred by the necessity to learn a new job, familiarize oneself with new colleagues and the new institution, and integrate the family into the new social, economic and educational structure. In this paper we examine the decision problems of people in these kinds of occupation. Specifically, we consider the polar case to that normally considered in the job-search literature; that is, we explore the case where it is costly to change jobs, but costless to search for them. This naturally focuses attention on the decision, once a new wage offer has been received, on whether to accept it (that is, to move) or to reject it (that is, not to move). An important feature of the model derived in this paper is that it allows for the possibility of on-the-job search; it is therefore capable of generating predictions consistent with the observed empirical phenomenon that the majority of job changes involve no intervening period of unemployment.' As Burdett (1977, 1978), one of the very few authors to model on-the-job search, remarks, such an empirical phenomenon cannot be explained by models that allow only for off-the-job search. is rather odd, therefore, that such models constitute the overwhelming majority of work in this area. The case that we are examining here was dismissed by Burdett (1977) as follows: It is reasonably straightforward to show that in this case an employed worker will accept another offer only if that offer is at least as great as his current wage offer plus some amount to repay him for the cost of removal (p. 37).