We present here, follow-up observations of four Binary black hole BBH eventsperformed with the High Energy Stereoscopic System (H.E.S.S.) in the Very HighEnergy (VHE) gamma-ray domain during the second and third LIGO/Virgoobservation runs. Detailed analyses of the obtained data did not showsignificant VHE emission. We derive integral upper limit maps considering ageneric E−2 source spectrum in the most sensitive H.E.S.S energy intervalranging from 1 to 10 TeV. We also consider Extragalactic Background Lightabsorption effects and derive integral upper limits over the full accessibleenergy range. We finally derive upper limits of the VHE luminosity for eachevent and compare them with the expected VHE emission from GRBs. Thesecomparisons allow us to assess the H.E.S.S. gravitational wave follow-upstrategies. For the fourth GW observing run O4, we do not expect tofundamentally alter our observing strategy, and will continue to prioritize skycoverage like for the previous runs<br
