To prove that it is possible to obtain many results (such as the asymptotic relations of Pameranchuk type, Froissart inequality, Martin theorem, etc.) of the analytical theory of elementary particles in any theory where the ordinary analyticity of dispersion amplitude is replaced by a certain generalized analyticity (such as the p-analyticity of Poloji, the generalized analyticity of Vekua). Hence we cannot consider these results as criteria for the validity of the analyticity at high energies. Therefore, in order to check the analyticity we ought to establish the relations which can not be deduced from any generalized analyticity, except ordinary analyticity.