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This study concentrates on the strategic interaction among suppliers in a centralized market where electrical energy and spinning reserve are simultaneously traded. A bilevel optimization technique and a mathematical program with equilibrium constraints approach are utilized to develop optimal bidding strategy for competitive suppliers participating in these markets. The strategic behavior of each supplier is represented via a parameterized Supply Function Equilibria (SFE) model. Two versions of the parameterized SFE are considered. They are referred to as c-parameterization model (involving manipulation of the sole intercept) and (s,c)-parameterization model (involving arbitrarily manipulation of the slope and the intercept). A pay-as-bid pricing mechanism is assumed for settling the market and calculating the supplier profit from selling energy and spinning reserve services. A six-bus test system together with a number of case studies are used to illustrate the interaction between the energy and spinning reserve markets. Transmission limits and the supplier physical constraints are observed in this study. The extension of the method to include a multiperiod market with intertemporal constraints is discussed through numerical results.