Searches for H Z production with the Higgs boson decaying into an invisible final state were performed using the data collected by the DELPHI experiment at centre-of-mass energies between 188 GeV and 209 GeV. Both hadronic and leptonic final states of the Z boson were analysed. In addition to the search for a heavy Higgs boson, a dedicated search for a light Higgs boson down to 40 GeV/c2 was performed. No signal was found. Assuming the Standard Model HZ production cross-section, the mass limit for invisibly decaying Higgs bosons is 112.1 GeV/c2 at 95% confidence level. An interpretation in the Minimal Supersymmetric extension of the Standard Model (MSSM) and in a Majoron model is also given.