In many scheduling applications it is required that the processing of some job be postponed until some other job, which can be chosen from a pregiven set of alternatives, has been completed. The traditional concept of precedence constraints fails to model such restrictions. Therefore, the concept has been generalized to so-called AND/OR precedence constraints which can cope with this kind of requirement. In the context of traditional precedence constraints, feasibility, transitivity, and the computation of earliest start times for jobs are fundamental, well-studied problems. The purpose of this paper is to provide efficient algorithms for these tasks for the more general model of AND/OR precedence constraints. We show that feasibility as well as many questions related to transitivity can be solved by applying essentially the same linear-time algorithm. In order to compute earliest start times we propose two polynomial-time algorithms to cope with different classes of time distances between jobs.