Let ℝëℝp denote the p-norm on ℝd, d≥2, 1•p••. For n points drawn independently and uniformly from the unit d-cube, the authors obtain the limit distribution of the largest nearest-neighbour link (with respect of ℝëℝp) in the cases (1) d=2, 1•p••; (2) d=3, p=1, 2, • and (3) d≥4, p=•.