The high-energy gamma-ray telescope EGRET observed the positions of two young pulsars, ${\rm PSR} \ 1951 + 32$ and $1509 - 58$, during its all-sky survey. Despite their youth and relative proximity to the Earth, neither pulsar is detected as a point source or in periodicity analysis. Flux limits of a few $\times 10^{-7}\ {\rm photon\enspace cm}^{-2} {\rm s}^{-1}$ are obtained for emission above 100 MeV, and $\sim 10^{-6}\ {\rm photon\enspace cm}^{-2} {\rm s}^{-1}$ for 30–100 MeV. For the conventional assumption of beaming into 1 sr, the flux limits suggest that less than 3.2 per cent of the radiation from ${\rm PSR} \ 1509-58$, and less than 1.8 per cent from ${\rm PSR} \ 1951 + 32$, is in the form of beamed high-energy gamma-rays. The ${\rm PSR} \ 1509 - 58$ limits lie approximately one order of magnitude below the extrapolated hard X-ray spectrum and suggest that the spectrum steepens in the MeV region.