In this note, structures of null solutions of the polynomial Dirac operators D-入, D^k , Dⁿ +E_f=0^n-1b_jd^j  are studied, where D is the Dirac operator in  R^m₁,入, b_j € C, j =0, ... , n-1, D⁰ =I .is the identity operator Explicit decompositions of null solutions of the polynomial Dirac operators in the respectively relevant subspaces are obtained which are used to derive their Taylor series expansions. The solutions of inhomogeneous equation p^(D)f=g are discussed for a special class of R^(M)-valued continuous functions g .