Exact average capacity results for L-branch coherent equal-gain combining (EGC) in correlated and uncorrelated fading channels are not known. This paper develops a novel framework (approach) for capacity analysis of L-branch EGC in generalized fading channels. In addition, Gamma shadowed generalized Nakagami-m fading model is proposed in order to statistically model the fading environments in high frequencies such as 60 GHz and above. Some simulations are carried out and then the obtained results are accentuated by means of numerical analysis based on the proposed framework. Numerical and simulation results, performed to verify the correctness of the proposed framework, are in perfect agreement.