  In this paper we define the generalized q-analogues of Euler sums and present
a new family of identities for q-analogues of Euler sums by using the method of
Jackson q-integral rep- resentations of series. We then apply it to obtain a
family of identities relating quadratic Euler sums to linear sums and
q-polylogarithms. Furthermore, we also use certain stuffle products to evaluate
several q-series with q-harmonic numbers. Some interesting new results and
illustrative examples are considered. Finally, we can obtain some explicit
relations for the classical Euler sums when q approaches to 1.
