Neutron-powder-diffraction data, collected with the D1B diffractometer, and single-crystal data, collected with the D10 four-circle diffractometer, both at the Institut Max von Laue-Paul Langevin, Grenoble, and single-crystal data, collected with the DN4 four-circle diffractometer at the Centre d'Etudes Nucleaires de Grenoble, show that MnWO4 (space group P2/c) undergoes three magnetic phase transitions below 14 K. The transition temperatures are 13.5 K (paramagnet-AF3), 12.3 K (AF3-AF2), and 8.0 K (AF2-AF1). Phases AF3 and AF2 are incommensurate with the crystallographic lattice. The propagation vector is k = (-0.214, 1/2, 0.457) in each case. In AF3 the magnetic moments order in the ac plane, whereas in AF2 an additional component in the [010] direction exists. The corresponding magnetic structures were found to be a sine wave in the case of AF3 and an elliptical spiral in the case of AF2. Other possibilities, like a simple spiral, a sine wave, and commensurate collinear spin arrangements, are also discussed for AF2. The magnetic structure in AF1 was refined based on a previously reported model. It is commensurate with a propagation vector k = (+/- 1/4, 1/2, 1/2). The magnetic moments are again collinear in the ac plane as in AF3, forming an angle of 37-degrees with the a axis.