The increasing penetration of inflexible and fluctuating renewable energy generation is often accompanied by a sequential market setup, including a day-ahead spot market that balances forecasted supply and demand with an hourly time resolution and a balancing market in which flexible generation handles unexpected imbalances closer to real-time and with a higher time resolution. Market characteristics such as time resolution, the time of market offering and the information available at this time, price elasticities of demand and the number of market participants, allow producers to exercise market power to different degrees. To capture this, we study oligopolistic spot and balancing markets with Cournot competition, and formulate two stochastic equilibrium models for the sequential markets. The first is an open-loop model which we formulate and solve as a complementarity problem. The second is a closed-loop model that accounts for the sequence of market clearings, but is computationally more demanding. Via optimality conditions, the result is an equilibrium problem with equilibrium constraints which we solve by an iterative procedure. When compared to the closed-loop solution, our results show that the open-loop problem overestimates the ability to exercise market power unless the market allows for speculation. In the presence of a speculator, the open-loop formulation forces spot and balancing market prices to be equal in expectation and indicates substantial profit reductions, whereas speculation has less severe impact in the closed-loop problem. We use the closed-loop model to further analyse market power issues with a higher time resolution and limited access to the balancing market.