In this paper we show how cointegration can be applied to capture the joint dynamics of multiple energy spot prices. For an example system we study the Title Transfer Facility, the Zeebrugge gas spot market and the National Balancing Point gas spot market, and, additionally, the Amsterdam Power Exchange power spot market, since these markets are strongly connected in terms of physical transportation and generation of power from gas. We develop a cointegrating multi-market model framework that is able to plausibly connect different singlemarket spot-price models. This is achieved by considering the mean-reverting spot-forward price spreads instead of spot prices only. Our analysis shows that the gas prices are strongly cointegrated, with a specific connection pattern for the markets, whereas cointegration of gas and power prices is at long-term forward price levels only.