The theory of stellar evolution can be more closely tested if we have the opportunity to measure new quantities. Nowadays, observations of galactic RR Lyr stars are available on a time baseline exceeding 100 years. Therefore, we can exploit the possibility of investigating period changes, continuing the pioneering work started by V. P. Tsesevich in 1969. We collected the available times of maximum brightness of the galactic RR Lyr stars in the GEOS RR Lyr database. Moreover, we also started new observational projects, including surveys with automated telescopes, to characterise the O-C diagrams better. The database we built has proved to be a very powerful tool for tracing the period variations through the ages. We analyzed 123 stars showing a clear O-C pattern (constant, parabolic or erratic) by means of different least-squares methods. Clear evidence of period increases or decreases at constant rates has been found, suggesting evolutionary effects. The median values are beta=+0.14 day/Myr for the 27 stars showing a period increase and beta=-0.20 day/Myr for the 21 stars showing a period decrease. The large number of RR Lyr stars showing a period decrease (i.e., blueward evolution) is a new and intriguing result. There is an excess of RR Lyr stars showing large, positive $beta$ values. Moreover, the observed beta values are slightly larger than those predicted by theoretical models.
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