Although the links between stratospheric dynamics, climate and weather have been demonstrated, direct observations of stratospheric winds are lacking, in particular at altitudes above 30 km. We report observations of winds between 8 and 0.01 hPa (similar to 35-80 km) from October 2009 to April 2010 by the Superconducting Submillimeter-Wave Limb-Emission Sounder (SMILES) on the International Space Station. The altitude range covers the region between 35-60 km where previous space-borne wind instruments show a lack of sensitivity. Both zonal and meridional wind components were obtained, though not simultaneously, in the latitude range from 30 degrees S to 55 degrees N and with a single profile precision of 7-9 ms(-1) between 8 and 0.6 hPa and better than 20 ms(-1) at altitudes above. The vertical resolution is 5-7 km except in the upper part of the retrieval range (10 km at 0.01 hPa). In the region between 1-0.05 hPa, an absolute value of the mean difference <2 ms(-1) is found between SMILES profiles retrieved from different spectroscopic lines and instrumental settings. Good agreement (absolute value of the mean difference of similar to 2 ms(-1)) is also found with the European Centre for Medium-Range Weather Forecasts (ECMWF) analysis in most of the stratosphere except for the zonal winds over the equator (difference >5 ms(-1)). In the mesosphere, SMILES and ECMWF zonal winds exhibit large differences (>20 ms(-1)), especially in the tropics. We illustrate our results by showing daily and monthly zonal wind variations, namely the semi-annual oscillation in the tropics and reversals of the flow direction between 50-55 degrees N during sudden stratospheric warmings. The daily comparison with ECMWF winds reveals that in the beginning of February, a significantly stronger zonal westward flow is measured in the tropics at 2 hPa compared to the flow computed in the analysis (difference of similar to 20 ms(-1)). The results show that the comparison between SMILES and ECMWF winds is not only relevant for the quality assessment of the new SMILES winds, but it also provides insights on the quality of the ECMWF winds themselves. Although the instrument was not specifically designed for measuring winds, the results demonstrate that space-borne sub-mm wave radiometers have the potential to provide good quality data for improving the stratospheric winds in atmospheric models.