Abstract. In recent years, there has been intensive research on the Q-linear relations between multiple zeta (star) values. In this paper, we prove many families of identities involving the q-analog of these values, from which we can always recover the corresponding classical identities by taking q → 1. The main result of the paper is the duality relations between multiple zeta star values and Euler sums and their q-analogs, which are generalizations of the Two-one formula and some multiple harmonic sum identities and their q-analogs proved by the authors recently. Such duality relations lead to a proof of the conjecture by Ihara et al. that the Hoffman ⋆-elements ζ ⋆ (s1, . . . , sr) with si ∈ {2, 3} span the vector space generated by multiple zeta values over Q.