A field containing 11 star and incipient star dunes occurs on Mars at 8.8°S, 270.9°W. Examples of linear dunes are found in a crater at 59.4°S, 343°W. While rare, dune varieties that form in bi- and multidirectional wind regimes are not absent from the surface of Mars. The occurrence of both of these dune fields offers new insight into the nature of martian wind conditions and sand supply, The linear dunes appear to have formed through modification of a formerly transverse aeolian deposit, suggesting a relatively recent change in local wind direction. The 11 dunes in the star dune locality show a progressive change from barchan to star form as each successive dune has traveled up into a valley, into a more complex wind regime. The star dunes corroborate the model of N. Lancaster (1989, Progr. Physical Geogr. 13, 67-91; 1989, Sedimentology 36, 273-289) for the formation of star dunes by projection of transverse dunes into a complex, topographically influenced wind regime. The star dunes have dark streaks emanating from them, providing evidence that the dunes were active at or near the time the relevant image was obtained by the Viking 1 orbiter in 1978. The star and linear dunes described here are located in different regions on the martian surface. Unlike most star and linear dunes on Earth, both martian examples are isolated occurrences; neither is part of a major sand sea. Previously published Mars general circulation model results suggest that the region in which the linear done field occurs should be a bimodal wind regime, while the region in which the star dunes occur should be unimodal. The star dunes are probably the result of localized complication of the wind regime owing to topographic confinement of the dunes. Local topographic influence on wind regime is also evident in the linear dune field, as there are transverse dunes in close proximity to the linear dunes, and their occurrence is best explained by funneling of wind through a topographic gap in the upwind crater wall.