To provide a method of producing a copper alloy smooth tube for a heat exchanger and a method of producing a copper alloy internally grooved tube for a heat exchanger by which a copper alloy tube having excellent brazability, and proof stress and fatigue strength before brazing heating and after brazing heating can be produced without causing the entanglement of oxide or the like, cracks or fractures and without causing the coarsening of crystal grains.

A billet having a composition comprising, by mass, 0.1 to 1.0% Sn, 0.005 to 0.1% P, ≤0.005% O and ≤0.0002% H, and the balance Cu with inevitable impurities is heated at 780 to 900°C, is hot-extruded, is thereafter water-cooled from ≥750°C so as to be cooled in such a manner that the average cooling rate to 100°C is controlled to ≥1.5°C/s, and is subsequently subjected to rolling at a working ratio of ≤92% and reduction working at a working ratio of ≤40% in succession.