Neutral-current four-fermion production, e+e−→fff′f′, is studied in 0.7 fb−1 of data collected with the L3 detector at LEP at centre-of-mass energies √s=183–209 GeV. Four final states are considered: qqνν, qqℓ+ℓ−, ℓ+ℓ−ℓ′+ℓ′− and ℓ+ℓ−νν, where ℓ denotes either an electron or a muon. Their cross sections are measured and found to agree with the Standard Model predictions. In addition, the e+e−→Zγ∗→fff′f′ process is studied and its total cross section at the average centre-of-mass energy 〈√s〉=196.6 GeV is found to be 0.29±0.05±0.03 pb0.29±0.05±0.03 pb, where the first uncertainty is statistical and the second systematic, in agreement with the Standard Model prediction of 0.22 pb. Finally, the mass spectra of the qqℓ+ℓ− final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found.