Streamflow　forecasting　using　interpretable　machine　learning　methods　(MLs)　for　exploring　runoff　processes　has　received　a　lot　of　attention.　However,　exploring　multi-step　ahead　daily　streamflow　forecasting　considering　antecedent　streamflow　as　an　input　for　various　interpretable　MLs　is　very　limited.　Thus,　three　interpretable　MLs　for　daily　streamflow　forecasting　in　the　Huaihe　River　basin　of　China　during　2002-2020,　including　eXtreme　Gradient　Boosting　(XGBoost),　long　short-term　memory　neural　network　(LSTM)　and　convolutional　neural　network　(CNN)　with　SHapley　Additive　exPlanations　(SHAP)　method,　were　implemented　to　study　the　role　of　potential　controlling　factors,　including　antecedent　streamflow,　soil　moisture　and　vegetation　growth,　in　runoff　processes　at　lead　times　of　0-6　days.　The　forecasting　performances　decreased　with　lead　times.　Specifically,　the　LSTM　model　performed　best　at　lead　times　of　0-3　days,　followed　by　CNN　and　XGBoost.　CNN　was　superior　to　LSTM　and　XGBoost　models　when　the　lead　time　was　greater　than　3　days.　The　optimal　forecasting　performances　were　0.71-0.97,　311.45-674.27　m3/s,　0.84-0.97　and　0.75-0.97　according　to　Nash-Sutclife　efficiency,　root-mean-square　error,　correlation　coefficient　and　Kling-Gupta　efficiency,　respectively.　The　interpretable　results　varied　across　different　MLs　and　at　different　lead　times.　The　antecedent　streamflow　consistently　dominated　the　runoff　processes,　particularly　in　the　LSTM　and　XGBoost　models.　However,　the　significant　role　of　soil　moisture　at　the　depth　of　28-100　cm　and　leaf　area　index　for　low　vegetation　gradually　emerged　with　increased　lead　times　for　CNN　models,　even　outranking　the　importance　of　antecedent　streamflow.　Furthermore,　the　interpretability　demonstrated　by　the　optimal　machine　learning　models　was　validated　through　the　infiltration　model　and　uncertainty　analysis.　Overall,　interpretable　machine　learning　has　great　potential　to　enhance　our　understanding　of　basin-scale　runoff　processes.