Abstract: In this paper we review existing loop scheduling algorithms and also describe the feedback-guided dynamic loop scheduling (FGDLS) algorithm that was proposed in Bull et al. [2] and Bull [1]. The FGDLS algorithm uses a feedback mechanism to schedule a parallel loop within a sequential outer loop. It has been shown to perform well for scheduling problems for which the load associated with the parallel loop changes relatively slowly as the outer sequential loop executes. However the question of convergence of the FGDLS algorithm has remained an open question. In this paper we are able to establish sufficient conditions (essentially requiring that the workload does not change too rapidly with loop iteration count) for the (global) convergence of a continuous analogue of the feedback-guided algorithm.