Neutral-current four-fermion production, e+e- → f ̄f f' ̄ 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: q ̄qν ̄ν, q ̄qℓ+ℓ-, ℓ+ℓ-ℓ'+ℓ'- and ℓ+ℓ-ν ̄ν, 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 ∗ → f ̄f f' ̄ 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 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 qq ̄ℓ+ℓ- final states are analysed to search for the possible production of a new neutral heavy particle, for which no evidence is found.