Mobile robots should perform a growing number of tasks and react to time-critical events. Thus, the ability to interrupt a task and resume it later is crucial. While interleaved execution occurs often in robotics, existing approaches do not consider the fact that interrupting a task and resuming an interrupted task often requires intermediate steps. In this paper we present an approach to interruptible task execution with resumption. We propose INTRGOLOG which extends INDIGOLOG by task interruption and resumption through introducing new constructs to determine and fulfill the requirements of tasks. Our experiments on a service robot and in simulation show that the ability to switch to another task enables a robot to react in a swift and reliable fashion to new events.