  We have searched for diphoton events (\ggmet) with large missing transverse
momentum, $\gamma\rlap{\kern0.25em/}E_T$ events (\gmetjj) with two or more
jets, and diphoton events ($\gamma\gamma$) with high transverse energies in
$p\bar p$ collisions at $\sqrt{s} = 1.8$ TeV using approximately 100~pb$^{-1}$
of data collected with the D\O detector at the Fermilab Tevatron in 1992--1996.
No excess of events beyond the expected backgrounds is observed. The null
results are interpreted in supersymmetric models with a dominant
$\tilde\chi^0_2\to\gamma\tilde\chi^0_1$ decay and in terms of Dirac pointlike
monopole production.
