Abstract : Deterministic approaches for source localization and extraction are desirable for short or nonstationary data, as opposed to techniques based on second or higher order statistics. Techniques based on tensor decompositions are recognized to be efficient in this framework, provided some diversity is available, in addition to time and space. With this goal, some authors have proposed to decompose a Space-Time-Frequency data tensor. In this paper, we propose a new multiway approach based on Space-Time-Wave-Vector (STWV) data which is obtained by a 3D local Fourier transform over space accomplished on the measured data. This method does not only permit to accurately localize sources even in a noisy environment, but simultaneously extracts the temporal behaviour associated with each source. The performance of this STWV analysis is investigated by means of computer simulations in the context of ElectroEncephaloGraphic (EEG) data analysis.