We study a class of q-analogues of multiple zeta values given by certain formal q-series with rational coefficients. After introducing a notion of weight and depth for these q-analogues of multiple zeta values we present dimension conjectures for the spaces of their weight-and depth-graded parts, which have a similar shape as the conjectures of Zagier and Broadhurst-Kreimer for multiple zeta values. n 1 >···>n l >0 1 n s 1 1 . . . n s l l .By s 1 + · · · + s l we denote its weight, by l its depth and we write Z for the Q-vector space spanned by all MZVs. It is a well-known fact that the space Z is a Q-algebra and that there are two different ways, known as respectively the stuffle and shuffle product formulas, which express the product of two MZVs as a Q-linear combination of MZVs.

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