Linear stability theory is used to study the effect of cross‐flow on Go¨rtler instability in incompressible boundary layers. The results cover a wide range of sweep angle, pressure gradient, and wall curvature parameters. It is shown that the cross‐flow stabilizes Go¨rtler disturbances by reducing the maximum growth rate and shrinking the unstable band of spanwise wave numbers. On the other hand, the effect of concave wall curvature on cross‐flow instability is destabilizing. Calculations show that the changeover from Go¨rtler to cross‐flow instabilities is a function of Go¨rtler number, pressure gradient, and sweep angle. The results demonstrate that Go¨rtler instability may still be relevant in the transition process on swept wings even at large angles of sweep if the pressure gradient is sufficiently small. The influence of pressure gradient and sweep can be combined by defining a cross‐flow Reynolds number. Thus, the changeover from Go¨rtler to cross‐flow instability takes place at some critical cross‐flow Reynolds number whose value increases with Go¨rtler number. ©1995 American Institute of Physics.