The increased presence of variable renewable generation drives a greater need for authorities to procure more ancillary services (AS) for grid balance. One of these services is contingency reserve (CR), which is used to regulate the grid frequency in contingencies. Many Independent System Operators (ISO) are structuring the rules of AS markets such that demand response (DR) can participate along side traditional supply-side resources. The available capacity of the generators can be used more efficiently for power production which they were designed for and not CR; cutting costs, and reducing pollution. As the ratio of inverter-based generation compared to conventional generation increases, the mechanical inertia used to stabilize frequency decreases. When coupled with the sensitivity of inverter-based generation to transient frequencies, the provision of ancillary services from other sources than generators becomes increasingly important. This paper provides a method to use AS for providing CR using DR to ensure system stability for a set of credible contingencies, while also satisfying economic and market goals. In the AS market, optimal power flow (OPF) is used to find the optimal offers/bids and transient behavior of frequency is considered. Our model separates DR into two categories-faster and slower-based on the deviation from the normal frequency of grid power. In a standard numerical example, we show that the proposed model can clear energy and ancillary service bids simultaneously while minimizing the total operating cost and satisfying transient frequency requirements. (C) 2016 Elsevier Ltd. All rights reserved.