Abstract <p>Knowledge of analytical properties of multiparticle amplitudes becomes increasingly important with increasing of accuracy of calculations in perturbation theory. Unfortunately, these properties are complex and poorly understood. One of important statements concerning these properties, is the absence of simultaneous discontinuities in energy invariants of overlapping channels. This statement is generally accepted and widely used now. To justify it, the Steinmann relations are used. We show that this statement is not correct. In particular, it contradicts the factorization of infrared singularities in gauge theories. We demonstrate explicitly existence of the simultaneous discontinuities and show illegitimacy of using the Steinmann relations to prove their absence. In the case of infrared singular parts of the amplitudes, their existence is completely natural. But it is not limited to such parts, and is not limited to the existence of infrared singularities at all, but occurs also in their absence. The consequence of this for further development of the BFKL approach is discussed.</p>