Spectrum sharing is a promising approach in cognitive radio networks to improve the spectrum utilization of wireless communication systems. In this paper, we analyze the performance of spectrum sharing systems under the peak interference constraint for a general fading model, namely the Alpha-Mu fading channel. In particular, we derive expressions for statistical characteristics such as probability density function and cumulative distribution function of the end-to-end signal-tonoise ratio for dissimilar parameter Mu. Using these statistics, we obtain the closed-form expressions for outage probability, amount of fading and approximate ergodic capacity for the considered spectrum sharing system. Finally, Monte Carlo simulations are presented to verify the analytical results.