A method for constructing a gauge-invariant transverse potential for vector vortex beams is proposed, based on a series expansion in the small parameter (?2⊥/k2)n. Explicit expressions are obtained for the values of the spin and orbital angular momenta, including higher-order corrections. It is shown that the ratio Jz/W generalizes the classical result for scalar vortices. The possibility of experimental investigation of orbital angular momentum in such beams is described.