The effect of annealing treatments on the normal plastic anisotropy (r-value) of a magnesium alloy, AZ61, processed by severe rolling was investigated. The various annealing treatments produce two effects on microstructure: grain coarsening and slight weakening of the texture. In addition, these treatments produce a noticeable decrease of the anisotropy that was correlated with an increase in strain rate sensitivity and a decrease of work hardening rate. It is concluded that an enhanced contribution of basal slip occurs as a consequence of the annealing treatments.