On a microscopic scale a ferromagnetic body is magnetically saturated and consists of regions in which the magnetization is uniform, separated by thin transition layers. Any stationary configuration corresponds to a minimum of an energy functional in which a small parameter \(\varepsilon\) is present. The asymptotic behaviour as \(\varepsilon\to 0\) is studied here. It is easy to see that any sequence of minimizers contains a subsequence \(M_{\varepsilon_ j}\) that converges to a field \(M\). By means of a \(\Gamma\)-limit procedure it is shown that this field \(M\) is a minimizer of a new functional containing a term proportional to the area of the surfaces separating different domains of uniform magnetization. The \(C^{1,y}\)-regularity of these surfaces, for \(\gamma<1/2\), is also proved under suitable assumptions for the external magnetic field.