The N¿el-Brown theory for superparamagnetic relaxation rates is generalized to ferromagnetic particles with mixed cubic and uniaxial anisotropy. In this article the uniaxial axis is in a ⟨001⟩ crystallographic direction, while in part 2 it is in a ⟨111⟩ direction. The calculations are for high energy barriers, so transitions between states (stable equilibria) are rare. Transition rates from an energy minimum across a saddle point are determined by the height of the energy barrier and the shape of the energy surface around these two points. To account for multiple connections between minima, a master equation is solved for the probability distribution and the effect on the magnetic moment is calculated. Some relaxation modes have no effect on the moment. There are as many as five distinct relaxation rates for the probability distribution, but at most two for the moment. One rate is for the component parallel to the uniaxial axis, while the other is for the perpendicular component. These rates are functions of the cubic anisotropy parameter K'1 and the uniaxial parameter Ku. The double relaxation rate can give rise to phenomena such as partial superparamagnetism and multiple blocking temperatures.