Based on analysis through barotropic shallow-water equations and baroclinic disturbance equations in the column coordinates,we achieve the results that the vortex Rossby Waves (VRW) of a typhoon are separated into two kinds.The first kind is generated owing to the second-order radial horizontal shear of tangential base flow or the radial change of vertical vorticity in it,i.e.,effects of β* as its root cause.The first kind of VRW (barotropic VRW) travels unidirectionally with respect to tangential base flow,with the direction dependent on the sign (plus or minus) of factor β*.When the vertical vorticity ζz of the base flow increases (decreases) in the radial r,the VRW of first kind propagates counterclockwise (clockwise) in the tangential.If a second- order vertical shear in the tangential base flow is allowed for,then the expression is found for phase speed of VRW of second kind (baroclinic VRW) in a typhoon,whose physical cause consists of a second-order vertical shear of wind speed in the tangential base flow or the z-axis inhomogeneity of mean vorticity in the radial r,i.e.,effects of β ** .The second kind of VRW propagates unidirectionally with respect to tangential base flow.When r increases (decreases) in the z direction,it travels clockwise (counterclockwise) with respect to 0.When mean wind speed in the tangential base flow undergoes a second-order radial horizontal shear or vertical shear,the wave in the typhoon is the mixed VRW and gravity waves.If windspeed of the tangential base flow experiences linear shear alone,with no second order shear happening,then no VRW occurs at all,implying the wave in a typhoon is solely internal inertia gravity wave.