[en] In order to derive information about the behaviour of strange Regge trajectories the detailed analysis of all available experimental data on hypercharge exchange reactions π⁺p → K⁺Σ⁺ and K^-p → π^-Σ⁺ in the 5-140 GeV energy range and square transferred momenta (-2-0) (GeV/c)² in the framework of the Regge model with taking into account secondary singularities has been made. Satisfactory description of experimental data has been achieved. More accurate values of parameters (intercepts and slopes) of the vector Ksub(V) and tensor Ksub(T) strange trajectories have been obtained. Dispersion analysis of the data on strange trajectories both in the scattering region and in the resonance region has been performed. The planar strange trajectory having a nonlinear behaviour in the -1< or approximately < or approximately 4 (GeV/c)² has been determined. This fact should be taken into account under the reconstruction of the interquark potentials