A search for stable and long-lived massive particles of electric charge |Q/e|=1 or 2/3, pair-produced in e+e− collisions at centre-of-mass energies from 130 to 183 GeV, is reported by the OPAL collaboration at LEP. No evidence for production of these particles was observed in a mass range between 45 and 89.5 GeV. Model-independent upper limits on the production cross-section between 0.05 and 0.19 pb have been derived for scalar and spin-1/2 particles with charge ±1. Within the framework of the minimal supersymmetric model (MSSM), this implies a lower limit of 82.5 (83.5) GeV on the mass of long-lived right- (left-)handed scalar muons and scalar taus. Long-lived charged leptons and charginos are excluded for masses below 89.5 GeV. For particles with charge ±2/3 the upper limits on the production cross-section vary between 0.05 and 0.2 pb. All limits, on masses and on cross-sections, are valid at the 95% confidence level for particles with lifetimes longer than 10−6 s.