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We formulate a model of pulsar spin evolution (braking, inclination angleevolution and radiative precession) taking into account the non-rigidity ofneutron star rotation. We discuss two simple limiting cases of this model andshow that the evolution of the inclination angle substantially depends on themodel of crust-core interaction. The non-rigidity of core rotation acceleratesthe inclination angle evolution and makes all pulsars evolve to the orthogonalstate. The size of the effect depends on the amount of differentially rotatingmatter and mechanism of its interaction with the rest of the star. Since therapid volution of the inclination angle apparently contradicts theobservational data, our results may be used as an additional test for thetheories of the cores of neutron stars.

The spin evolution of the pulsars with non-rigid core