Many Feynman diagrams contribute to four-fermion production in $e^+e^-$ collisions in addition to the pair production of W and Z bosons. 0.7 fb$^{-1}$ of LEP data at centre-of-mass energies up to 209 GeV are analysed. An inclusive measurement of the production cross section of final states with hadrons and leptons, hadrons and missing energy, leptons and leptons and missing energy is described. The particular case of a production mediated by a Z boson and a virtual photon is singled out. Results are compared with the Standard Model expectations.