A general network model with finitely or infinitely many activities is considered. Each activity may require several storable resources. Fixed resource amounts are delivered at fixed times. Necessary and sufficient conditions are given so that for a system of start times and durations of the activities no lack of resources appears at any time, and a method is presented to determine such a system, Further, the paper deals with the case random resource requirements. For this ease, resource requirements are estimated, and the probability that, at any time, there appears no lack of resources for a system of start times and durations is considered. Finally, it is described how to treat the case where also non-storable resources have to be taken into account.