The electron paramagnetic resonance (EPR) spectra of the (eta(6)-C6H6)V, (eta(6)-C6D6)V transients and (eta(6)-C6H6)(2)V, (eta(6)-C6D6)(2)V molecules are obtained by codepositing C6H6 and C6D6 with vanadium atoms in an Ar matrix at 15 K. Under optimal experimental conditions, the spectra of these axial species are well resolved and the elusive parallel resonance components are identified for the first time. Mathematical expressions for the resonance field positions and line shapes are derived and are used to simulate the experimental spectra. For (eta(6)-C6H6)V and (eta(6)-C6D6)V the g and vanadium hyperfine tensors are diagonal with g(xx) g(yy) = 1.942(3), g(zz) = 2.007(3), A(xx)(V) = A(yy)(V) = -113.2(5) x 10(-4) cm(-1), and A(zz)(V) = -9.3(5) x 10(-4) cm(-1). The (eta(6)-C6H6)V and (eta(6)-C6D6)V effective spin Hamiltonian tensor components and resonance field positions are also derived in terms of their molecular orbital (MO) coefficients assuming a (2)A(1) ground state. Consequently, the g, hyperfine, and superhyperfine tensor components, obtained from the simulation of the experimental spectra, are compared with those computed using the local-density-functional method. The very good agreement between the experimental and computed parameters indicate that the (eta(6)-C6H6)V and (eta(6)-C6D6)V complexes have (2)A(1) ground states. The explicit formulas derived for the carbon and hydrogen hyperfine tensors, using symmetry adapted linear combinations of atomic orbitals, imply that they are not diagonal and do not have coincident principal axes. Although this suggests that, in principle, the carbon and hydrogen centers in (eta(6)-C6H6)V and (eta(6)-C6D6)V must be magnetically inequivalent, the resulting effects are negligible due to the small 2p (C) character of the 10a(1) singly occupied molecular orbital. Understanding and simulating the (eta(6)-C6H6)V and (eta(6)-C6D6)V EPR spectra is essential in the analysis of the EPR spectra of more complicated molecules like (eta(6)-C6H3F3)V, (eta(6)-C6F6)V, and (eta(6)-C6F6)(2)V.