  Following an idea of Nigel Higson, we develop a method for proving the
existence of a meromor-phic continuation for some spectral zeta functions. The
method is based on algebras of generalized differential operators. The main
theorem states, under some conditions, the existence of a meromor-phic
continuation, a localization of the poles in supports of arithmetic sequences
and an upper bound of their order. We give an application in relation with a
class of nilpotent Lie algebras.
