Based on the new two-state theory of curve crossing recently completed by the authors, a compact and powerful theory is formulated for a general resonant multi-channel scattering with nonadiabatic tunneling (NT) type curve crossings. This theory is demonstrated to work remarkably well by comparing with the numerical solutions of close-coupling equations. Even detailed structures of overlapping resonances are nicely reproduced by the theory. Furthermore, this theory is very simple, not requiring any nonunique diabatization procedure, any complex calculus and any information on the couplings, neither diabatic nor nonadiabatic. The theory is based only on the adiabatic potentials on the real axis. Together with the previously proposed theory for the Landau-Zener (LZ) type curve crossings, the present semiclassical theory provides a complete picture of and a very powerful tool for multi-channel curve crossing problems.