Automatic Modulation Classification is a key technology in Cognitive Radio Networks. Blind identification of the modulation scheme of an unknown detected signal has various commercial and military applications. Performance of Automatic Modulation Classifiers degrades severely under low Signal-to-Noise ratios and fading channel scenarios. Cooperative classification is presented as a means to enhance the classification performance as well as to relax the computational constraints on individual nodes. In this work, the performance of cooperative cumulants-based modulation classification is studied under flat Rayleigh fading channels. The degradation in performance of a single node under flat Rayleigh fading is first presented in comparison to Additive White Gaussian Noise channels. Next, performance improvement obtained through cooperative combining of classification data from several nodes is presented. Analytical results as well as simulations show that cooperation will improve the overall performance of modulation classifiers, overcoming the performance loss due to fading and reaching classification results comparable to the AWGN scenario.