Abstract: The stability testing of 2-Dimensional recursive digital filters had been a very hot problem in 1970`s and 80`s. The right solution is not available though some researchers have been working on this problem even now. We have proposed in this paper a new test procedure (may be an alternative to Jury-Marden algorithm) to test the stability of 1-D recursive digital filters. We also gave for a restricted order 2-D digital filters, a method to test the stability of the given transfer function which is devoid of nonessential singularities of the second kind. In both the 1-D and 2-D cases the available methods of evaluating the complex integrals for variance is used to conclude about the stability of the filter.