The classification of Cartan type modular Lie superalgebras is the key of the classification of Lie superalgebras over a fields of prime characteristic. The Recognition Theorem established foundation for the classification of Lie algebras over a fields of prime characteristic. According to the theories on adjoint modules of Cartan type modular Lie algebras in Recognition Theorem

we study the adjoint modules of Cartan type modular Lie superalgebras W(n). By virtue of the direct sum decomposition of the Z2-graded components in W(n)

we obtain two types of adjoint module

analyse the relationship between them

and prove their irreducibilities.