In this paper, we examine nonlinear interrelationship between energy consumption and output level for a panel of G7 countries. For this purpose, we propose a nonlinear cointegration test in heterogeneous panels for testing the presence of a cointegrating relationship that follows a globally stationary exponential smooth transition (ESTR) process, and apply our test for investigating long-run relationship between energy use and economic growth in the case of the G7 countries. Our results suggest the presence of a long-run relationship between these two variables whereas adjustment to the equilibrium is inherently nonlinear. After establishing long-run relationship between energy consumption and output, we estimate a Panel Smooth Transition Vector Error Correction Model and apply nonlinear Granger causality tests in order to analyze the direction of the causality between these variables. We find that the causality between energy consumption and output level is dependent on the phases of business cycle. Our results highlight importance of taking account of possible nonlinearities in analysing output-energy causality nexus and designing energy policies.