In a previous paper (6) we have studied those minimal surfaces which admit geodesic mappings without isometries or similarities on another, not necessarily minimal, surface. Here we determine all pairs of minimal surfaces which can be geodesically mapped on each other. We find that two such surfaces are either:
(i) similar Bonnet associates of each other, or
(ii) both Poisson surfaces (that is, isometric to a plane), or
(iii) both Scherk surfaces (2).