Abstract Analytical models for the primary and secondary instabilities of three-dimensional boundary layer are developed by assuming locally parallel shear flow and scale similarity at each position. More specifically, both linear and nonlinear growth rates of the stationary crossflow modes are estimated as functions of a normalized wavenumber and a Reynolds number, which are locally defined by the characteristic velocity and length scales of the inflectional profile of shear flow. By choosing one of them as the primary mode, the maximum linear growth rate of the secondary mode is also estimated by assuming scale similarity. The quantitative expressions of these scaling laws are determined so that they agree with several results of direct numerical simulation and numerical stability analysis. Transition to turbulence is triggered when a secondary mode grows nonlinearly. In other words, if a nonlinear primary mode is less unstable to secondary instability, it may not cause transition but laminarize the boundary layer. For various three-dimensional boundary layers, our models are expected to be useful for quickly predicting whether a certain crossflow mode leads to transition or laminarization under a certain disturbance level.KeywordsBoundary layer transitionCrossflow instabilitySecondary instability