Flight Crew Multiengine; Flight Crew Instrument; Flight Crew Air Transport Pilot (ATP)
Aircraft Equipment Problem Less Severe; Flight Deck / Cabin / Aircraft Event Smoke / Fire / Fumes / Odor; Flight Deck / Cabin / Aircraft Event Illness / Injury
General Physical Injury / Incapacitation
Aircraft
Immediately after gear retraction on the flight; the FO and I smelled a very strong odor of fumes that I would describe as dirty socks and an oily smell. We donned oxygen masks. A few minutes later; I briefly raised my mask off my face and could no longer detect any unusual odors. On approach into ZZZ1; we smelled the fumes again; and donned oxygen masks. However; this time the fumes were not as strong as on takeoff. In hindsight; it is clear that the better decision than continuing the flight would have been to return to the departure airport. The FO has communicated with me several times since then; advising that he has experienced headaches since this fume event occurred.
A330 Captain reported smelling a strong odor and fumes after takeoff; and then again on descent to a lesser degree.