This paper presents a new modelling framework for day–ahead electricity prices based on multivariate Lévy semistationary (MLSS) processes. Day–ahead prices specify the prices for electricity delivered over certain time windows on the next day and are determined in a daily auction. Since there are several delivery periods per day, we use a multivariate model to describe the different day–ahead prices for the different delivery periods on the next day. We extend the work by Barndorff-Nielsen et al. (2010) on univariate Lévy semistationary processes to a multivariate setting and discuss the probabilistic properties of the new class of stochastic processes. Furthermore, we provide a detailed empirical study using data from the European Energy Exchange (EEX) and give new insights into the intra–daily correlation structure of electricity day–ahead prices in the EEX market. The flexible structure of MLSS processes is able to reproduce the stylized facts of such data rather well. Furthermore, these processes can be used to model negative prices in electricity markets which started to occur recently and cannot be described by many classical models.