Lifetimes of excited states of the phosphorus isotopes 33 , 34 , 35 , 36 15 P have been measured by using the differential recoil-distance method. The isotopes of phosphorus were populated in binary grazing reactions initiated by a beam of 36 S ions of energy 225 MeV incident on a thin 208 Pb target mounted in the Cologne plunger apparatus. The combination of the PRISMA magnetic spectrometer and an early implementation of the AGATA γ -ray tracking array was used to detect γ rays in coincidence with projectile-like nuclear species. Lifetime measurements of populated states were made within the range from about 1 to 100 ps. The number of states for which lifetime measurements were possible was limited by statistics. For 33 P , lifetime limits were determined for the first 3/2+ and 5/2+ states at 1431 and 1848 keV, respectively; the results are compared with previous published lifetime values. The lifetime of the first 2+ state of 34 P at 429 keV was determined and compared with earlier measurements. For 35 P , the states for which lifetimes, or lifetime limits, were determined were those at 2386, 3860, 4101, and 4493 keV, with Jπ values of 3/2+, 5/2+, 7/2− 1 , and 7/2− 2 , respectively. There have been no previous published lifetimes for states in this nucleus. A lifetime was measured for the stretched π ( 1 f 7 / 2 ) ⊗ ν ( 1 f 7 / 2 ) J π = ( 7 + ) state of 36 P at 5212 keV and a lifetime limit was established for the stretched π ( 1 d 3 / 2 ) ⊗ ν ( 1 f 7 / 2 ) J π = ( 5 − ) state at 2030 keV. There are no previously published lifetimes for states of 36 P . Measured lifetime values were compared with the results of state-of-the-art shell-model calculations based on the PSDPF effective interaction. In addition, measured branching ratios, published mixing ratios, and electromagnetic transition rates, where available, have been compared with shell-model values. In general, there is good agreement between experiment and the shell model; however there is evidence that the shell-model values of the M1 transition rates for the 3/2+1→ 1 / 2 + (ground state) and 5/2+1→ 3 / 2 + 1 transitions in 33 P underestimate the experimental values by a factor between 5 and 10. In 35 P there are some disagreements between experimental and shell-model values of branching ratios for the first and second excited 7/2− states. In particular, there is a serious disagreement for the decay characteristics of the second 7/2− state at 4493 keV, for which the shell-model counterpart lies at 4754 keV. In this case, the shell-model competing electromagnetic decay branches are dominated by E1 and M1 transitions.