Multivariate Lévy processes are tools suitable for modeling risk when jumps and sudden large values may occur.Since these processes are entirely specified by their distribution over one fixed time horizon,the most suggesting way of modeling their dependence is to choose a time horizon and to combine the marginal distributions of the process by a copula function.However,although this approach seems simple,it has a number of serious drawbacks.The copula has to be chosen such that the resulting multivariate distribution is infinitely divisible,which may be very complicated to ensure.Furthermore,the distribution of the process on other time horizons may become untractable if it is not stable under convolution.For these reasons,the concept of Lévy copulas,which does not suffer from the mentioned drawbacks,has been introduced.Unfortunately,the number of parametric Lévy copulas presented in the literature is rather small which limits their use in risk management applications.In this paper,we propose an alternative way of modeling dependence in multivariate Lévy processes which combines the advantages of both mentioned approaches.It bases on the idea of Lévy copulas,but uses common copula functions to ensure a rich variety of models.Furthermore,any marginal Lévy processes and any copula may be combined to a proper multivariate Lévy process.