A new multivariate curve resolution method is presented and tested with data of various levels of complexity. Rotational and intensity ambiguities and the effect of selectivity on resolution are the focus. Analysis of simulated data provides the general guidelines concerning the conditions for uniqueness of a solution for a given problem. Multivariate curve resolution is extended to the analysis of three-way data matrices. The particular case of three-way data where only one of the orders is common between slices is studied in some detail.