  The Shapiro Phase Shift on Pulsars (SPSP) influence at low , but detectable
level the pulsars' (PSR) periods and their derivatives. This effect may be
already written in PSRs' time derivative deviation and in particular it may
explain the presence of a few negative pulse derivatives among 558 known PSRs.
We describe in detail the phenomenon and predict that the SPSP may play a role
in period derivative deviations for just a few PSRs a year ( 0.5 - 5 ev / yr)
at a positive period derivative 10^-14 - 10^-15 s/s level , leading to a
plausible explanation to the puzzling negative pulse derivative of few PSRs'
periods.
