  We study the stau lifetime in a scenario with the LSP taken to be a
neutralino and the NLSP being a stau, based on the minimal supersymmetric
Standard Model. The mass difference between the LSP and NLSP, $\delta m$, must
satisfy $\delta m/m_{\tilde{\chi}} \sim$ a few % or less for coannihilation to
occur, where $m_{\tilde{\chi}}$ is the neutralino mass. We calculate the stau
lifetime from the decay modes $\tilde{\tau}\to \tilde{\chi}\tau$,
$\tilde{\chi}\nu_\tau\pi$, and $\tilde{\chi}\nu_\tau\mu(e)\nu_{\mu(e)}$ and
discuss its dependence on various parameters. We find that the lifetime is in
the range $10^{-22}$--$10^{16}$ sec for $10^{-2} \le \delta m \le 10$ GeV. We
also discuss the connection with lepton flavor violation if there is mixing
between sleptons.
