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Theoretical estimates of the rates of radial pulsation period change inGalactic Cepheids with initial masses 5.5M_\odot <= Mzams <= 13M_\odot,chemical composition X=0.7, Z=0.02 and periods 1.5 day <= P <= 100 day areobtained from consistent stellar evolution and nonlinear stellar pulsationcomputations. Pulsational instability was investigated for three crossings ofthe instability strip by the evolutionary track in the HR diagram. The firstcrossing occurs at the post-main sequence helium core gravitational contractionstage which proceeds in the Kelvin--Helmholtz timescale whereas the second andthe third crossings take place at the evolutionary stage of thermonuclear corehelium burning. During each crossing of the instability strip the period ofradial pulsations is a quadratic function of the stellar evolution time.Theoretical rates of the pulsation period change agree with observations butthe scatter of observational estimates of dP/dt noticeably exceeds the width ofthe band (\delta\log |dP/dt| <= 0.6) confining evolutionary tracks in theperiod - period change rate diagram. One of the causes of the large scatterwith very high values of dP/dt in Cepheids with increasing periods might be thestars that cross the instability strip for the first time. Their fractionranges from 2% for Mzams=5.5M_\odot to 9% for Mzams=13M_\odot. Variable stars\alpha UMi and IX Cas seem to belong to such objects.

Theoretical rates of pulsation period change in the Galactic Cepheids