A　totally　asynchronous　gradient　algorithm　with　fixed　step　size　is　proposed　for　federated　learning.　A　mathematical　model　is　presented　and　a　convergence　result　is　established.　The　convergence　result　is　based　on　the　concept　of　macro　iterations　sequence.　The　interest　of　the　contribution　is　to　show　that　the　asynchronous　federated　learning　method　converges　when　gradients　of　loss　functions　are　updated　by　workers　without　order　nor　synchronization　and　with　possible　unbounded　delays.　　©　2024　IEEE.