  Theoretical estimates of the rates of radial pulsation period change in
Galactic 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 are
obtained from consistent stellar evolution and nonlinear stellar pulsation
computations. Pulsational instability was investigated for three crossings of
the instability strip by the evolutionary track in the HR diagram. The first
crossing occurs at the post-main sequence helium core gravitational contraction
stage which proceeds in the Kelvin--Helmholtz timescale whereas the second and
the third crossings take place at the evolutionary stage of thermonuclear core
helium burning. During each crossing of the instability strip the period of
radial pulsations is a quadratic function of the stellar evolution time.
Theoretical rates of the pulsation period change agree with observations but
the scatter of observational estimates of dP/dt noticeably exceeds the width of
the band (\delta\log |dP/dt| <= 0.6) confining evolutionary tracks in the
period - period change rate diagram. One of the causes of the large scatter
with very high values of dP/dt in Cepheids with increasing periods might be the
stars that cross the instability strip for the first time. Their fraction
ranges 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.
