We describe the entire phase structure of a large number of colour generalized Yang–Mills theories in 1 + 1 dimensions. This is illustrated by the explicit computation for a quartic plus quadratic model. We show that the Douglas–Kazakov and cut-off transitions are naturally present for generalized Yang–Mills theories separating the phase space into three regions: a dilute one a strongly interacting one and a degenerate one. Each region is separated into sub-phases. For the first two regions the transitions between sub-phases are described by the Jurkiewicz–Zalewski analysis. The cut-off transition and degenerated phase arise only for a finite number of colours. We present second-order phase transitions between sub-phases of the degenerate phase.