  In this paper we prove the strong $q$-log-convexity of the Eulerian
polynomials of Coxeter groups using their exponential generating functions. Our
proof is based on the theory of exponential Riordan arraya and a criterion for
determining the strong $q$-log-convexity of polynomials sequences, whose
generating functions can be given by the continued fraction. As consequences,
we get the strong $q$-log-convexity the Eulerian polynomials of type $A_n,B_n$,
their $q$-analogous and the generalized Eulerian polynomials associated to the
arithmetic progression $\{a,a+d,a+2d,a+3d,\ldots\}$ in a unified manner.
