We investigate performance of the both variable and fixed-gain amplify-and-forward cooperative communication systems over composite fading and shadowing channels modeled by independent but not necessarily identically distributed generalized-K distribution. We consider two different Nth best path selection schemes: the Nth best relay and link selection. In the Nth best relay selection (RS) scheme, signals received from the Nth best relay and the direct path are combined with maximal-ratio combining and decoded at the destination. In the Nth best link selection (LS) scheme, the direct path is included to the selection set and only the signal received from the selected path is decoded at the destination. New symbol error rate (SER) expressions are derived analytically by using the moment generating function (MGF) approach with Pade approximation and the cumulative distribution function approach. The MGF and SER expressions are in closed-form for the Nth best RS and LS systems, respectively. The derived SER expressions are almost exact at any signal-to-noise ratio. We also present the asymptotic diversity order of the system. The analytical results are verified by Monte-Carlo simulations. Since the generalized-K channel model is a quite general channel model, the existing symbol error probability results given in the literature for cooperative systems with path selection over conventional Rayleigh or Nakagami-m fading channels can be obtained as special cases of our results. Crown Copyright (C) 2015 Published by Elsevier Ltd. on behalf of The Franklin Institute. All rights reserved.