By constantly monitoring at least one complete hemisphere of the sky, neutrino telescopes are
well designed to detect neutrinos emitted by transient astrophysical events. Real-time searches for neutrino candidates coincident with Swift and Fermi gamma-ray bursts, IceCube high energy neutrino events and gravitational wave (GW) candidates observed by LIGO/Virgo are performed with the ANTARES telescope. By requiring temporal coincidence, this approach increases the sensitivity and the significance of a potential discovery. The latest results of these analyses will be presented, with emphasis on the results of the neutrino follow-up of IceCube very high-energy neutrino events and LIGO/Virgo GW public events during the run O3. In case of a coincident detection, the position of the GW source on the sky would be largely constrained thanks to the better angular accuracy of ANTARES compared to the GW detectors, bringing valuable information for subsequent electromagnetic follow-ups. In case of no coincidence, an upper limit on the neutrino fluence and the total energy emitted in neutrinos will be provided for each studied alert.