The effects of anisotropic hyperfine interactions on the recombination reactions of spin correlated radical pairs in a weak applied magnetic field are discussed in the context of the radical pair mechanism (RPM). Model calculations are presented for radical pairs containing a single spin-1/2 nucleus with an axial or rhombic coupling to one of the Impaired electrons. The so-called low field effect (LFE) and various resonances in the magnetic field effect (MFE) are calculated. Approximate analytical expressions are given for the field positions of the resonances which are shown to arise from energy level crossings.