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 ktons yr. For the hep neutrino search, two events are observed in the effective electron energy range of 14:3 MeV < TeA < 20 MeV, where 3.1 background events are expected. After accounting for neutrino oscillations, an upper limit of 2:3 ; 10 cm 2 s 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 < TeA < 35MeV, and, consequently, an upper limit on the e component of the DSNB flux in the neutrino energy range 1 Department of Physics and Astronomy, Laurentian University, Ramsey Lake Road, Sudbury, ON P3E 2C6, Canada. 2 Department of Physics, Queen’s University, Kingston, ON K7L 3N6, Canada. 3 Department of Physics, University of Texas at Austin, Austin, TX 78712-0264. 4 Department of Physics and Astronomy, University of Pennsylvania, Philadelphia, PA 19104-6396. 5 Ottawa-Carleton Institute for Physics, Department of Physics, Carleton University, Ottawa, ON K1S 5B6, Canada. 6 Institute for Nuclear and Particle Astrophysics and Nuclear Science Division, Lawrence Berkeley National Laboratory, Berkeley, CA 94720. 7 Physics Department, University of Guelph, Guelph, ON N1G 2W1, Canada. 8 Department of Physics, University of Oxford, Denys Wilkinson Building, Keble Road, Oxford OX1 3RH, UK. 9 Los Alamos National Laboratory, Los Alamos, NM 87545. 10 Current address: Goldman Sachs, 85 Broad Street, New York, NY 10004. 11 Center for Experimental Nuclear Physics and Astrophysics and Department of Physics, University of Washington, Seattle, WA 98195. 12 Current address: Physics Department, Princeton University, Princeton, NJ 08544-0708. 13 Sudbury Neutrino Observatory Laboratory, P.O. Box 146, Lively, ON P3Y 1M3, Canada. 14 Current address: Department of Physics, University of California, Irvine, CA 92697. 15 Laboratory for Nuclear Science, Massachusetts Institute of Technology, Cambridge, MA 02139. 16 Department of Physics and Astronomy, Louisiana State University, Baton Rouge, LA 70803. 17 Chemistry Department, Brookhaven National Laboratory, Upton, NY 11973-5000. 18 Current address: Graduate School of Engineering, Hiroshima University, Hiroshima 739-8526, Japan. 19 Tri-University Meson Facility, 4004 Wesbrook Mall, Vancouver, BC V6T 2A3, Canada. 20 Department of Physics and Astronomy, University of British Columbia, Vancouver, BC V6T 1Z1, Canada. 21 Laboratório de Instrumentação e Fı́sica Experimental de Partı́culas, 1000-149 Lisboa, Portugal. 22 Current address: Fermi National Accelerator Laboratory, Batavia, IL 60510. 23 Current address: Department of Physics, University of Liverpool, Liverpool L69 7ZE, UK. 24 Current address: Department of Physics, University of Chicago, Chicago, IL 60637. 25 Current address: Lawrence Livermore National Laboratory, Livermore, CA 94551. 26 Current address: Remote Sensing Laboratory, P.O. Box 98521, Las Vegas, NV 89193. 27 Rutherford Appleton Laboratory, Chilton, Didcot OX11 0QX, UK. 28 Also at: Imperial College, London SW7 2AZ, UK. 29 Current address: Department of Physics and Astronomy, University of Sussex, Brighton BN1 9QH, UK. 1545 The Astrophysical Journal, 653:1545Y1551, 2006 December 20 # 2006. The American Astronomical Society. All rights reserved. Printed in U.S.A.