  A search has been made for neutrinos from the hep reaction in the Sun and
from the diffuse supernova neutrino background (DSNB) using data collected
during the first operational phase of the Sudbury Neutrino Observatory, with an
exposure of 0.65 kilotonne-years. For the hep neutrino search, two events are
observed in the effective electron energy range of 14.3 MeV <T_eff< 20 MeV
where 3.1 background events are expected. After accounting for neutrino
oscillations, an upper limit of 2.3x10^4 cm^-2s^-1 at the 90% confidence level
is inferred on the integral total flux of hep neutrinos. For DSNB neutrinos, no
events are observed in the effective electron energy range of 21 MeV <T_eff< 35
MeV and, consequently, an upper limit on the nu_e component of the DSNB flux in
the neutrino energy range of 22.9 MeV <E_nu< 36.9 MeV of 70 cm^-2s^-1 is
inferred at the 90% confidence level. This is an improvement by a factor of 6.5
on the previous best upper limit on the hep neutrino flux and by two orders of
magnitude on the previous upper limit on the $\nu_e$ component of the DSNB
flux.
