We calculate limits to the properties of massive, unstable neutrinos using data from {gamma}-ray detectors on the Pioneer Venus Orbiter (PVO) Spacecraft. The absence of a {gamma}-ray signal in the PVO detector constrains the branching ratio to photons (B{sub {gamma}}), mass (m{sub {nu}}), and radiative lifetime ({tau}{sub {gamma}}={tau}/B{sub {gamma}}). For low-mass (m{approx_lt}T{approximately}8MeV) neutrinos decaying {nu}{r_arrow}{nu}{sup {prime}}{gamma}, B{sub {gamma}}{lt}3{times}10{sup {minus}7} for m{sub {nu}}{tau}{approx_lt}10{sup 6}keVsec, and B{sub {gamma}}{lt}2{times}10{sup {minus}13}m{sub {nu}}{tau}/keVsec for m{sub {nu}}{tau}{approx_gt}10{sup 6}keVsec; limits for high-mass neutrinos are somewhat weaker due to Boltzmann suppression. We also calculate limits for decays that produce {gamma} rays through the bremsstrahlung channel, {nu}{r_arrow}{nu}{sup {prime}}e{sup +}e{sup {minus}}{gamma}. With one exception, the PVO limits are roughly comparable to those from an analysis of data from the Solar Max Mission (SMM) Satellite (which observed at higher {gamma}-ray energies but for a much shorter time). For neutrino mass states that are nearly degenerate, {delta}m{sup 2}/m{sup 2}{approximately}0.1{lt}1, our limits for the mode {nu}{r_arrow}{nu}{sup {prime}}{gamma} become more stringent by a factor as large as m{sup 2}/{delta}m{sup 2}, because more decay photons are shifted into the PVO energy window. For this same reason, SMM cannot constrain this case. {copyright} {ital 1997} {ital The American Physical Society}