  The Baikal-GVD deep underwater neutrino experiment participates in the
international multi-messenger program on discovering the astrophysical sources
of high energy fluxes of cosmic particles, while being at the stage of
deployment with a gradual increase of its effective volume to the scale of a
cubic kilometer. In April 2021 the effective volume of the detector has been
reached 0.4 km3 for cascade events with energy above 100 TeV generated by
neutrino interactions in Lake Baikal. The alarm system in real-time monitoring
of the celestial sphere was launched at the beginning of 2021, that allows to
form the alerts of two ranks like "muon neutrino" and "VHE cascade". Recent
results of fast follow-up searches for coincidences of Baikal-GVD high energy
cascades with ANTARES/TAToO high energy neutrino alerts and IceCube GCN
messages will be presented, as well as preliminary results of searches for high
energy neutrinos in coincidence with the magnetar SGR 1935+2154 activity in
period of radio and gamma burst in 2020.
