We show that a strong system of derivations ${D_0, D_1,cdots,D_m}$ on a commutative Banach algebra A is contained in the radical of A if it satisfies one of the following conditions for separating spaces; (1) $partial(D_i) subseteq rad(A) and partial(D_i) subseteq K D_i(rad(A))$ for all i, where $K D_i(rad(A)) = {x in rad(A))$ : for each $m geq 1, D^m_i(x) in rad(A)}$. (2) $(D^m_i) subseteq rad(A)$ for all i and m. (3) $ar{xpartial(D_i)} = partial(D_i)$ for all i and all nonzero x in rad(A).