This research addresses the problem of tracking a moving point target in a time sequence of hyperspectral images; we focus on the detection of moving targets with staring technologies. In these applications, the images consist of targets moving at subpixel velocity in backgrounds that are influenced by both evolving clutter and noise. The demand for a low false-alarm rate on one hand and a high probability of detection on the other makes the tracking a challenging task. The use of hyperspectral images should be superior to current technologies, due to the benefit of simultaneously exploiting two target-specific properties: the spectral target characteristics and the time-dependent target behavior. We propose an algorithm that is in two steps. The first step is the transformation of each of the hyperspectral images forming the sequence into a two-dimensional image using a known point-target detection-acquisition algorithm. In the second step, target detection and tracking are performed by the means of time-domain processing. A match-filter technique is used for the hyperspectral image transformation; a variance-filter algorithm is developed to detect the presence of targets from the temporal profile of each pixel while suppressing clutter-specific influences.