The paper presents heuristics for two types of resource—constrained project-scheduling problems: the problem of levelling the resources consumption and the minimum project—duration problem. Both minimal and maximal time lags between the start of successive activities of the project in question are permitted. Such a project can be modelled by an activity-on-node network containing cycles. For the resource—levelling problem with maximal time lags, neither exact algorithms nor heuristic procedures have been proposed so far. Two different heuristic procedures are presented. The sequential or direct method processes the nodes or respectively activities of the cyclic project network successively without scheduling the strong components of the network separately. The contraction method firstly finds a feasible subschedule for each strong component of the cyclic network and secondly replaces each strong component by a single node. The resulting (contracted) acyclic network is treated by the direct method. An empirical analysis shows that for the minimum project—duration problem, the contraction method is markedly superior to the direct method. For the resource—levelling problem, both approaches behave similarly.