Let $S(z_1,z_2),;S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ be power series with operator coefficients such that $S_(z_1,;z_2)=S_1(z_1,z_2)S_2(z_1,z_2)$. Assume that the multiplications by $S_1(z_1,z_2)$ and $S_2(z_1,z_2)$ are contractive transformations in H($mathbb{D}^2,;mathcal{C}$). Then the factorizations of spaces $mathcal{D}(mathbb{D},; ilde{S})$ and $mathcal{D}(mathbb{D}^2,mathcal{S})$ are well-behaved.