In this paper, we analyze the fading statistics of a generic fading distribution, termed the N-product Generalized Nakagami-m (GNM) distribution (N*GNM distribution), constructed as the product of the power of N statistically independent and non-identically distributed GNM random variables, for the purpose of modeling the cascaded fading channels. In particular, using the Fox's H function, we derive the probability density function, the cumulative distribution function, the moment generating function and the moments of such channels in closed-form. These derived results are a convenient tool to statistically model the cascaded GNM fading channels and to analyze the performance of digital communication systems over these kinds of channels. As such, generic closed-form expressions for the amount of fading, the outage probability, the capacity, the outage capacity and the average bit error probabilities of digital communications systems over cascaded GNM fading channels are presented. Numerical and simulation results, performed to verify the correctness of the proposed formulation, are in perfect agreement.