In this contribution, we present the follow-up of several recent IceCube alerts, using the complementarity of the two neutrino detectors of KM3NeT: ORCA and ARCA, that cover together an energy range from few GeV to tens of PeV. At the time of the particular alerts, both detectors were in operation with partial configurations. The follow-up has been performed by looking for a signal excess in an on-off analysis around the IceCube best-fit position or the best AGN counterpart position, depending on the alert. A time period of ±1 day around the IceCube alerts, as well as an extended search time window of 1 month, have been analysed. The analyses and their results, including statistical significance, discovery potential and flux upper limits, will be reported here.