The nonclassical potential symmetries of some nonlinear partial differential equations and nonclassical symmetries of them were researched. New potential symmetries of one equation and new symmetries of these original equations were obtained. Nonclassical symmetries of auxilary potential systems were also determined. Furthermore, the corresponding similarity solutions can be obtained by using some of the above symmetries. The solutions have extensive application value for further researching the physical phenomena described by the nonlinear partial differential equations.