Abstract: In multi-moded real-time systems there may exist a different set of tasks per mode. During its mission, the system may switch to a new operating mode, which will involve completing running old-mode tasks and starting new-mode tasks. This represents a transient, bounded overload, which may not be schedulable unless some new-mode tasks are delayed until the old-mode load has decreased. Although this idea has already been proposed elsewhere, a method for obtaining the shortest offsets that make a transition schedulable has not yet been devised. The management of shared resources during the transition represents an added problem to tackle. This paper presents a new mode change protocol and an algorithm to calculate the necessary offsets to schedule mode changes according to a set of requirements and in the presence of shared resources.