Summary In this paper we derive the time pattern of optimal planned expenditures for R and D projects in which the total effort required to complete the research satisfactorily is not known. Theorem 1 summarizes our results under alternative assumptions regarding the behavior of the function governing the supposed probability of completing the R and D satisfactorily with incremental effort. In addition, an easily employed necessary condition for the R and D project to be worthwhile is provided in Theorem 2.