We present limits on anomalous $\mathrm{WWZ}$ and $\mathrm{WW}\ensuremath{\gamma}$ couplings from a search for $\mathrm{WW}$ and $\mathrm{WZ}$ production in $p\overline{p}$ collisions at $\sqrt{s}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}1.8\mathrm{TeV}$. We use $p\overline{p}\ensuremath{\rightarrow}e\ensuremath{\nu}\mathrm{jjX}$ events recorded with the D0 detector at the Fermilab Tevatron Collider during the 1992--1995 run. The data sample corresponds to an integrated luminosity of $96.0\ifmmode\pm\else\textpm\fi{}5.1{\mathrm{pb}}^{\ensuremath{-}1}$. Assuming identical $\mathrm{WWZ}$ and $\mathrm{WW}\ensuremath{\gamma}$ coupling parameters, the 95% C.L. limits on the $\mathrm{CP}$-conserving couplings are $\ensuremath{-}0.33<\ensuremath{\lambda}<0.36$ $(\ensuremath{\Delta}\ensuremath{\kappa}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0)$ and $\ensuremath{-}0.43<\ensuremath{\Delta}\ensuremath{\kappa}<0.59$ $(\ensuremath{\lambda}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}0)$, for a form factor scale $\ensuremath{\Lambda}\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2.0\mathrm{TeV}$. Limits based on other assumptions are also presented.