[en] Spin correlations at the detection of nonfactorizable two-particle spin states are analyzed. The appearance of such correlations is connected with the general quantum-mechanical effect predicted by Einstein, Podolsky, and Rosen. In the presence of the spin correlations the scattering of one of two unpolarized final particles results in the polarization of the other (unscattered) particle. That makes it possible to prepare particle beams with controlled spin polarization without the direct action on the particle to be polarized. Specific features of correlations in singlet and triplet states of two particles with spin 1/2 are discussed. The correlations of the polarizations of two identical nucleons (protons, neutrons) with small relative momenta and neutron-proton spin correlations at the deuteron breakup are considered. It is shown that the spins of the final particles from the reaction π⁺ + ⁴He → ³He + p are strongly correlated. The correlations of the secondary scattering planes for two particles with spin 1/2, scattered on spinless or unpolarized target, are studied