Summary: We extend the result of J. G. Gaines [ibid. 49, No. 3/4, 169-179 (1994; Zbl 0827.60038)] to show that Lyndon set forms an algebraic basis for the set of multiple stochastic integrals with respect to Brownian motions and Poisson processes, so that any multiple stochastic integral can be expressed as a polynomial of Lyndon basis. The result for Philip Hall basis is similar. From the computational point of view, the adoption of either of the bases has the same effect on reducing much computing work of the numerical approximation for stochastic differential equations of jump-diffusion type.