As a result of a pseudosymmetry search, the double perovskite compounds Sr2MWO6 (M = Ni, Zn, Co, Cu) were identified as good candidates for presenting Landau-type phase transitions at high temperatures. In the present work, the phases observed at different temperatures are reported and the phase transitions are discussed. The Sr2MWO6 (M = Ni, Zn, Co) compounds present I4/m–Fmm phase transitions, while Sr2CuWO6 shows an I4/m–I4/mmm phase transition. All these transitions are second order and are consistent with the pseudosymmetry concept. Sr2ZnWO6 and Sr2CoWO6 also show P21/n–I4/m phase transitions and Sr2CuWO6 presents a phase transition of the type I4/mmm–Fmm. These transitions are first order. Alongside the experimental results a discussion of some aspects of the study of phase transitions in double perovskite materials is presented.