Predicting electricity prices and demand is a very important issue for the energy market industry. In order to improve the accuracy of any predictive model, a previous variable importance analysis is highly advised. In this paper, we propose an alternative framework to assess the variable importance in multivariate response scenarios based on the permutation importance technique, applying the Conditional inference trees algorithm and a ? -divergence measure. Our solution was tested in simulated examples as well as a real case, where we assessed and ranked the most relevant predictors for price and demand of electricity jointly in the Spanish market. The new method outperforms, in most cases, the outcomes achieved by the recently proposed techniques, Intervention prediction measure (IPM) and Sequential multi-response feature selection (SMuRFS). For the electricity market case, we identified the most relevant predictors among pollutant, renewable, calendar and lagged prices variables for the joint response of demand and price, showing also the effectiveness of the proposed multivariate response method when compared with the univariate response analysis.