Idealised uniaxial stable single-domain (SD) particles permit only two possible stable positions in which the magnetic moment can lie, either closely parallel or anti-parallel to the particle long (easy) axis. This implicit two state feature has never been challenged in real acicular "uniaxial" SD particles. We now demonstrate that such "uniaxial" particles can allow several quantifiable stable (or metastable) orientations of the magnetic moment within the same particle. A new model is presented with quantitative predictions verified by experiments. The results have important implications for rock magnetism, palaeomagnetism, and magnetic materials research. Firstly, the new model quantitatively accounts for several previously unexplained diverse phenomena exhibited by such SD particles, including the acquisition of gyroremanences, field-impressed anisotropy, and transverse components of remanence in individual particles. These phenomena are theoretically impossible in idealised uniaxial SD particles, and could now be used to quantify the deviation of real particles from ideal behaviour. Secondly, deflections of the natural remanence vector and computations of the ancient field vector and palaeointensity are not only controlled by the shape and distribution of the particles, but also by the possible stable orientations of the moments within single-domain particles. The model is also relevant to other single-domain particle morphologies. © 2005 IOP Publishing Ltd.