Context : The Helios measurements of the angular momentum flux L of the fast solar wind lead to a tendency for the fluxes associated with individual ion angular momenta of protons and alpha particles , L _ { p } and L _ { \alpha } , to be negative ( i.e. , in the sense of counter-rotation with the Sun ) . However , the opposite holds for the slow wind , and the overall particle contribution L _ { P } = L _ { p } + L _ { \alpha } tends to exceed the magnetic contribution L _ { M } . These two aspects are at variance with previous models . Aims : We examine whether introducing realistic ion temperature anisotropies can resolve this discrepancy . Methods : From a general set of multifluid transport equations with gyrotropic species pressure tensors , we derive the equations governing both the meridional and azimuthal dynamics of outflows from magnetized , rotating stars . The equations are not restricted to radial flows in the equatorial plane but valid for general axisymmetric winds that include two major ion species . The azimuthal dynamics are examined in detail , using the empirical meridional flow profiles for the solar wind , constructed mainly according to measurements made in situ . Results : The angular momentum flux L is determined by the requirement that the solution to the total angular momentum conservation law is unique and smooth in the vicinity of the Alfvén point , defined as where the combined Alfvénic Mach number M _ { T } = 1 . M _ { T } has to consider the contributions from both protons and alpha particles . Introducing realistic ion temperature anisotropies may introduce a change of up to 10 \% in L and up to \sim 1.8 km~ { } s ^ { -1 } in azimuthal speeds of individual ions between 0.3 and 1 AU , compared with the isotropic case . The latter has strong consequences on the relative importance of L _ { P } and L _ { M } in the angular momentum budget . Conclusions : However , introducing ion temperature anisotropies can not resolve the discrepancy between in situ measurements and model computations . For the fast-wind solutions , while in extreme cases L _ { P } may become negative , L _ { p } never does . On the other hand , for the slow solar wind solutions examined , L _ { P } never exceeds L _ { M } , even though L _ { M } may be less than the individual ion contribution , since L _ { p } and L _ { \alpha } always have opposite signs for the slow and fast wind alike .