Based on the effective-mass approximation, the energy spectrum of the free Aexcitonstatesofcadmiumsulphideisstudied. Thestarkeffect inanelectric field, theZeeman effect and the diamagnetic interaction in a magnetic field of the A-exciton states are analysed by using a novel perturbative-variational approach. The results are compared with experimental data and previous calculations using different approaches. Our results are in good agreement with previous work and our method is much more efficient.