A specific mechanism of mode coupling in a waveguide propagation is studied when two range-dependent eigenvalues approach each other. This phenomenon is analogous to the so-called quasi-crossing of states in atomic physics (Landau-Zener theory). It is considered for the sound wave propagation in a coastal wedge in the presence of a sound-speed profile. The change in mode composition and the corresponding spatial variability of the sound field are analyzed by using modes coupling equations and the parabolic equation with a field decomposition over adiabatic modes, respectively.