Abstract: A horizontal component of the earth's rotation(?*=2Ωcosφ) is included in a set of linearized β-plane equations, which have a constant horizontal component of the Coriolis parameter, while the vertical component varies with latitude. This feature of the equations enables the vorticity and angular momentum principles to hold in their usual form, to study the influence of the ?*-effect on waves on the equatorial-plane. The results show that the ?*-effect can be important if the perturbations are the function of latitude. Although ?* has no effects on the frequencies of the mixed Rossby-gravity and Rossby waves, it modifies their am plitude. We also find that when the perturbations are independent of latitude(e. g. Kelvin waves), the ?*-effect disappears.