Single-particle resonances in deformed nuclei are considered using the coupled-channel Schro¨dinger equation method with the outgoing boundary conditions. Two variants of this method are investigated: the non-adiabatic one (based on the weak-coupling scheme) and the adiabatic one (based on the strong coupling). The R-matrix theory and the Gamow state approach are discussed and compared with each other. It is shown that the widths of very narrow proton resonances can be calculated by combining the harmonic oscillator expansion method with the R-matrix approach. ©2000 American Institute of Physics.