The object of this paper is to investigate the analytic continuation and asymptotic expansions for families of the generalized Hurwich-Lerch Zeta functions defined by Srivastava et al. [24]. The result obtained is of general character and includes, as special cases, the same fashion results the Gauss hypergeometric function, the generalized hypergeometric function and for the Fox-Wright function given earlier by Kilbas et al. [14] and others.