The time evolution of the orthogonal spatially homogeneous Bianchi type-II models is analysed by applying qualitative techniques to the reduced and regularised differential system of Rosquist and Jantzen (1988). This enables the author to obtain the asymptotic behaviour of solutions near the initial singularity and in the distant future. A global picture emerges in which the general orthogonal type-II solution is shown to be spiralling about the non-LRS solution found by Collins (1971). The author also gives an example how one can obtain exact solutions with help of the series method developed by Picard (1928).