  In this talk I discuss some scenarios which involve small extensions of the
ideas usually considered in the Minimal Supersymmetric Standard Model (MSSM). I
present results of a study of the implication of non-universal gaugino masses
(NGM) for the invisible decays of the lightest scalar and the correlation of
the same with the relic density of the lightest supersymmetric particle (LSP)
in the Universe. Further I discuss SUSY with \rpv. Decay of $\tilde \chi_1^0$
in the case of dominant \rpv and \LV, trilinear $\lambda$ and $\lambda'$
couplings, and also that of $\tilde \chi_1^0, \tilde \chi_1^+$ caused by the
bilinear \rpv, \LV couplings are discussed. The effect of the latter for the
trilepton signal at the Tevatron is presented. I end with a discussion of
signals of Heavy Majorana Neutrinos (HMN) at the LHC.
