The motion of electron spins in anisotropic systems described by spin Hamiltonians containing zero-field tensors is described in terms of semi-classical trajectories constructed either in spin space from surfaces of constant energy or in energy space from surfaces of constant magnitude of the spin angular momentum. The trajectories are presented as time-independent projections for a range of values of the non-axial orthorhombic spin-Hamiltonian parameterE. Analogies are made to the closely related semi-classical description of the rotational motion of spherical symmetric and asymmetric top molecules. The spin-Hamiltonian parameters of a number of organic and inorganic systems are used to illustrate the results.