Vanadium oxides have attracted considerable attention, not only due to their potential technological applications, but also because of the rich variety of structures and compositions they may adopt. This proposal explores the magnetic dynamics in the vanadium oxides rutile VO2 and bronze VO2(B) as a function of temperature as they undergo structural changes. Accompanying these structural transformations are large changes in resistivity which continue to attract attention in the literature. By using muons, we want to examine the changes in magnetic behaviour in a series of samples (bulk and nanosized rutile VO2 and nanosized VO2(B)) in an effort to better understand the mechanisms ongoing in these important materials and to check what effect, if any, size has on their magnetic behaviour.