The \ensuremath{\gamma}-ray transitions in the ground-state bands of $^{238}\mathrm{Pu}$ and $^{239}\mathrm{Pu}$ up to spins ${26}^{+}$ and 51/${2}^{+}$, respectively, were observed in the reaction $^{239}\mathrm{Pu}$${+}^{117}$Sn (${\mathit{E}}_{\mathrm{c}.\mathrm{m}.}$=422.9 MeV). Another band in $^{239}\mathrm{Pu}$ was observed, and is tentatively identified as the high-spin continuation of the ${0}^{\mathrm{\ensuremath{-}}}$ octupole excitation built on the 1/${2}^{+}$ ground band in $^{239}\mathrm{Pu}$. The measured \ensuremath{\gamma}-ray multiplicity and total energy provided data on the population of entrance states in both $^{238}\mathrm{Pu}$ and $^{239}\mathrm{Pu}$. The one-neutron-transfer cross section, as determined by the yield of the ${6}^{+}$\ensuremath{\rightarrow}${4}^{+}$ transition in $^{238}\mathrm{Pu}$, was measured to be 65\ifmmode\pm\else\textpm\fi{}25 mb. This transition yield is estimated to represent between 80% and 90% of the total one-neutron-transfer cross section.