Harmonizable processes form a wide class of nonstationary processes, which admit a convenient Fourier analysis and have spectral distributions characterized by correlated components. They are proved to be useful in many fields of application, for example, recently they were successfully applied in the analysis of replicated ElectroEncephaloGram signals for studying the brain connectivity. In this paper, we introduce a parametric form for these harmonizable processes, namely Harmonizable Vector AutoRegressive and Moving Average models (HVARMA). In the same spirit as of standard VARMA models, they are derived as a unique solution of a difference equation based on a properly defined concept of harmonizable noise. We exhibit their spectral characteristics and provide a way to generate realizations from a given HVARMA model.