We study minimal homeomorphisms (all orbits are dense) of the tori T-n, n <= 4. The linear part of a homeomorphism phi of T-n is the linear mapping L induced by phi on the first homology group of T-n. It follows from the Lefschetz fixed point theorem that 1 is an eigenvalue of L if phi minimal. We show that if phi is minimal and n <= 4. then L is quasi-unipontent, that is, all of the eigenvalues of L are roots of unity and conversely if L is an element of GL(n, Z) is quasi-unipotent and 1 is an eigenvalue of L, then there exists a C-infinity minimal skew-product diffeomorphism phi of T-n whose linear part is precisely L. We do not know whether these results are true for n >= 5. We give a sufficient condition for a smooth skew-product diffeomorphism of a torus of arbitrary dimension to be smoothly conjugate to an affine transformation.