The different relaxation processes that connect the four energy levels in phosphorus doped silicon have been investigated experimentally. The relaxation time ${T}_{s}$ ($\ensuremath{\Delta}{m}_{s}=\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\Delta}{m}_{I}=0$) was found to be independent of phosphorus concentration below \ensuremath{\sim}${10}^{16}$ P/${\mathrm{cm}}^{3}$. Its value at 3200 oersteds and 1.25\ifmmode^\circ\else\textdegree\fi{}K was \ensuremath{\sim}3\ifmmode\times\else\texttimes\fi{}${10}^{+3}$ seconds and varied as $\frac{1}{T}$ for $1.3\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl2\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$ and as $\frac{1}{{T}^{7}}$ for $2.5\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}lTl4.2\ifmmode^\circ\else\textdegree\fi{}\mathrm{K}$. The magnetic field dependence in the $\frac{1}{T}$ region suggests a direct phonon process. In the $\frac{1}{{T}^{7}}$ region ${T}_{s}$ was independent of the magnetic field between 3000 and 8000 oersteds. Above a concentration of ${10}^{16}$ P/${\mathrm{cm}}^{3}$ ${T}_{s}$ varied rapidly with donor concentration, dropping to ${10}^{\ensuremath{-}4}$ seconds at 3\ifmmode\times\else\texttimes\fi{}${10}^{17}$ P/${\mathrm{cm}}^{3}$. In this concentration dependent region ${T}_{s}$ was independent of the magnetic field but depended on the number of acceptors present. None of the ${T}_{s}$ mechanisms can at present be accounted for by the theories of Pines, Bardeen, and Slichter, and Abrahams. The relaxation time ${T}_{x}$ ($\ensuremath{\Delta}{m}_{s}=\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\Delta}{m}_{I}=\ensuremath{\mp}1$) was \ensuremath{\sim}30 hours at 3000 oersteds and \ensuremath{\sim}5 hours at 8000 oersteds in fair agreement with the theory of PBS. The relaxation time ${T}_{N}$ ($\ensuremath{\Delta}{m}_{I}=\ifmmode\pm\else\textpm\fi{}1$, $\ensuremath{\Delta}{m}_{s}=0$) at 1.25\ifmmode^\circ\else\textdegree\fi{}K exceeded 10 hours.