A search is performed for Higgs bosons decaying into invisible final states, produced in association with a Z(0) boson in e(+)e(-) collisions at energies between 183 and 209 GeV. The search is based on data samples collected by the OPAL detector at LEP corresponding to an integrated luminosity of about 660 pb(-1). The analysis aims to select events containing the hadronic decay products of the Z(0) boson and large missing momentum, as expected from Higgs boson decay into a pair of stable weakly interacting neutral particles, such as the lightest neutralino in the Minimal Supersymmetric Standard Model. The same analysis is applied to a search for nearly invisible Higgs boson cascade decays into stable weakly interacting neutral particles. No excess over the expected background from Standard Model processes is observed. Limits on the production of invisibly decaying Higgs bosons produced in association with a Z(0) boson are derived. Assuming a branching ratio BR(h(0) -> invisible) = 1, a lower limit of 108.2 GeV is placed on the Higgs boson mass at the 95% confidence level. Limits on the production of nearly invisibly decaying Higgs bosons are also obtained. (C) 2009 Elsevier B.V. All rights reserved.