The present invention relates to monoclonal antibodies that bind or neutralize Orthopoxviruses. The invention provides such antibodies, fragments of such antibodies retaining B5 or A33 binding ability, fully human antibodies retaining B5 or A33 binding ability, and pharmaceutical compositions including such antibodies. The invention further provides for isolated nucleic acids encoding the antibodies of the invention and host cells transformed therewith. Additionally, the invention provides for prophylactic, therapeutic, and diagnostic methods employing the antibodies and nucleic acids of the invention.