This paper deals with integration of energy storage systems into electricity markets. We explain why the energy storage systems increase flexibility of both power systems and energy markets and why such flexibility is desirable, particularly when variable renewable energy sources are being used in existing power systems. As opposed to the existing literature, our model includes a dual technology energy storage system, acting in two different markets. We introduce a mathematical formulation for this model applied to two Dutch electricity markets. Adopting optimal control approach with the goal to maximize the yearly benefit, we show that the dual energy storage system can be profitable already when the same buying/selling strategies are adopted for the working days and weekends. We show that the profitability (slightly) increases with different buying/selling strategies for the weekdays and weekends. Finally, we demonstrate how the yearly benefit varies with size and efficiency of the devices chosen and market prices.