A micromagnetic theory is presented for spin-reorientation transitions in ultrathin magnetic films with normal surface anisotropy. Both discrete and continuum models are investigated and coincidence is found between the results derived from them. Two continuous transitions in spin orientation, from uniform and normal to canting, and then to uniform and in-plane, are observed as the film thickness is increased. The effects of higher-order terms in the expansions of the anisotropies compared to the dominant terms are also considered. A method for evaluating the surface anisotropy is formulated. The relation between the present micromagnetic theory and the phenomenological theory is discussed.