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The Shapiro Phase Shift on Pulsars (SPSP) influence at low , but detectablelevel the pulsars' (PSR) periods and their derivatives. This effect may bealready written in PSRs' time derivative deviation and in particular it mayexplain 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 rolein 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 aplausible explanation to the puzzling negative pulse derivative of few PSRs'periods

Gravitational Shapiro phase shift on the period of the pulsars to detect dark matter