A search has been performed for pair-production of stable and long-lived massive particles with charge $|Q/e|=1$ and fractional charges of $|Q/e|=$ 2/3, 4/3 and 5/3, using the data collected by the OPAL experiment at energies significantly above the Z$^0$ peak, for a total integrated luminosity of ~690~pb$^{-1}$. No evidence for the production of such particles was observed. Cross section limits have been set for particles of different charges, and mass limits obtained for left- and right-handed smuons and staus within the framework of the MSSM.