In molecules, the nonadiabatic couplings between two adiabatic potentials build the avoided crossing (AC) region. The rovibronic resonances in the AC region of two-coupled potentials are very special, since they are not in the bound state region of the adiabatic potentials, and they usually do not play important roles on the scatterings and are less discussed. Exemplified in particle scattering, resonances in the AC region are comprehensively investigated. The effects of resonances in the AC region on the scattering cross sections strongly depend on the nonadiabatic couplings of the system, it can be very significant as sharp peaks, or inconspicuous buried in the background. More importantly, it shows a simple quantity proposed by Zhu and Nakamura (1992 J. Chem. Phys. 97 8497) to classify the coupling strength of nonadiabatic interactions, can be well applied to quantitatively estimate the importance of resonances in the AC region. Example applications of the quantity for real molecules (MgH, CO and OH) can well explain the evolutions of cross sections in the AC region published in the literatures. This work provides a simple and practical way to determine the candidate molecules when studying the resonances in the AC region.