The coherent inelastic processes of the type a→b, which may take place in the collisions of hadrons and γ-quanta with nuclei at very high energies (the nucleus remains the same), are theoretically investigated. The influence of matter inside the nucleus is taken into account by using the optical model based on the concept of refraction index. Analytical formulas for the effective cross-section σ
coh(a→b) are obtained, taking into account that at ultrarelativistic energies the main contribution into σ
coh(a→b) is provided by very small transferred momenta in the vicinity of the minimum longitudinal momentum transferred to the nucleus.