Linear dunes occur on planetary surfaces, including Earth, Mars, and Titan, yet their dynamics are poorly understood. Recent studies of terrestrial linear dunes suggest they migrate by elongation only in supply-limited environments. Here, we investigate elongating linear dunes in the Hellespontus Montes region of Mars which are morphologically similar to terrestrial systems. Multitemporal, high-resolution orbital images show these linear dunes migrate by elongation only and that the fixed sediment source of the dunes probably restricts any lateral migration. Some linear dunes maintain their along-length volume and elongate at rates comparable to adjacent barchans, whereas those which decrease in volume show no elongation, suggesting they are near steady state, matching morphometric predictions. Limited sediment supply may restrict Martian linear dunes to several kilometers, significantly shorter than many terrestrial linear dunes. Our results demonstrate the close similarities in dune dynamics across the two planetary surfaces. Plain Language Summary Linear dunes are elongated sand ridges found on Earth, Mars, and Titan and form in areas with at least two wind directions. The way in which linear dunes move is poorly understood, in particular whether they migrate parallel or perpendicular to their ridge crests. Recent investigations have suggested that linear dunes on Earth migrate parallel to their ridge crests in areas with a fixed source of limited sand. The surface of Mars is a natural laboratory for investigating linear dunes. We use time series, high-resolution orbital images to investigate the migration of Martian linear dunes. Like those on Earth, the Martian linear dunes also originate from a fixed sand source and grow parallel to their crests only. Furthermore, we also show that the linear dunes no longer grow as they approach a steady state. Our results demonstrate strong similarities in the behavior of dunes on Mars and Earth.