Limited knowledge exists on complementary methodology for effective studying cultivar adaptive responses in two-factorial multi-environment trials planned in split-block design. The main objective of this paper, as the first - mostly methodological - part of the further studies, was to present and empirically illustrate the using, and to assess the usefulness of statistical methods for studying the adaptive yield response of winter wheat cultivars to agricultural environments and to two crop management intensities, on the basis of data from oneyear multi-environment two-factorial trials arranged in a split-block design. The statistical methodology consists of the combined three-way analysis of variance according to the fixed-effects model for the cultivar × management x location (GxMxL) grain yield data from this series of trials, the AMMI analysis of the cultivar × location (G×L) interaction and the cluster analysis for the AMMI-modeled means of the cultivars at the test locations calculated across two crop management intensities. The suggested methodology was an effective tool for identifying various patterns of cultivar response to environments and to the intensity of crop managements. It permits effective identifying cultivars exhibiting wide or narrow adaptation. Wide adaptation exhibited by the Polish cultivar Bogatka and the German cultivar Jenga, losing in only very few environments the top two positions for yield to other groups of cultivars with specific adaptation or generally not adapted.