Some reports of Langmuir circulations describe windrows at systematic angles to the local wind direction. Other observers find windrows in close alignment to the wind direction, but with a systematic drift sideways to the wind. These effects probably result from more than one physical cause. Here it is shown, by an analysis of the linear stability of the surface layer, averaged to remove surface wave fluctuations, that persistent small windrow angles can result from weak stable density stratification. In these cases, the linearly most unstable modes are found to be weakly three dimensional for the range of parameters considered. Possible surface windrow patterns include rolls mostly parallel to the wind but of finite length, with branching and merging, as well as parallel rolls inclined to the wind and drifting laterally with respect to the wind direction. For unstratified flow, steady two-dimensional rolls are preferred. ¿ American Geophysical Union 1993