We propose a method for detecting and tracking the motion of a large number of moving objects in crowded environments, such as concourses in railway stations or airports, shopping malls, or convention centers. Unlike many methods for motion detection and tracking, our approach is not based on vision but uses 2D range images from a laser rangefinder. This facilitates the real-time capability of our approach, which was a primary goal. The time-variance of an environment is captured by a sequence of temporal maps, which we denoted as time stamp maps. A time stamp map is a projection of a range image onto a two-dimensional grid, where each cell which coincides with a specific range value is assigned a time stamp. Based on this representation we devised two very simple algorithms for motion detection and motion tracking. Our approach is very efficient, with a complete cycle involving both motion detection and tracking taking 6 ms on a Pentium 166Mhz.