A search for scalar particles and neutralinos such as those predicted
by supersymmetric models has been performed using a data sample of 4.4
million hadronic Z(0) decays recorded by the OPAL detector at the e()e(-) collider LEP. The production of such particles typically leads t
o event topologies consisting of an acoplanar pair of jets, or of a mo
no-jet, accompanied by sizeable missing energy owing to neutrinos and
other undetectable neutral particles. Limits are obtained, at the 95%
confidence level, on the masses and production rates of scalar particl
es produced in association with the Z(0). Limits are also placed on ne
utralino production, for which an additional possible signature is als
o studied, events containing a single observed photon. Within the Mini
mal Supersymmetric Standard Model, the mass of the lightest neutralino
is found to be larger than 12.5 GeV/c(2) at 95% C.L., provided that t
an beta is larger than 1.5.