Performance of cooperative spatial multiplexing systems over composite channels is presented. In particular, we derive the exact closed-form average symbol error rate (SER) expressions for cooperative spatial multiplexing systems with linear equalization receiver (e.g., Zero-Forcing) and M-ary modulation scheme in the composite channel of log-normal shadowing and Rayleigh fading. Using the Gauss-Hermite quadrature integration, the average SER is expressed in the forms of Appell hypergeometric function. Applying the series representation of Appell hypergeometric function, we derive a very tight approximation for the average SER. We also perform Monte-Carlo simulations to validate our analysis.