The local atomic structure and dynamics in multiferroic MnWO4 and Mn0.7Co0.3WO4 have been studied by X-ray absorption spectroscopy at the Co(Mn) K-edge and W L-3-edge. The analysis of the first coordination shell of metal ions using single-shell Gaussian approximation and regularization-like method allowed us to determine a distortion of Mn(Co)O-6 and WO6 octahedra. It was found that the local environment of Co2+ ions in Mn0.7Co0.3WO4 is close to that in CoWO4, whereas the presence of cobalt ions reduces the distortion of MnO6 octahedra in comparison with pure MnWO4.