The concentration dependences of the effective permittivity of an anisotropic composite containing co-directional particles in the form of oblate or elongated ellipsoids of rotation – spheroids – in the dielectric matrix are obtained. The calculation is made by the numerical solution of a system of coupled quadratic and integral equations obtained by a strict modification of the quasi-static Bruggeman theory. It is shown that the traditional (simplified) modification of the Bruggeman theory, widely used for calculating anisotropic composites, gives errors of different signs for the longitudinal and transverse polarization of electromagnetic waves relative to the axis of spheroids. In this case, the dependences of errors on the concentration of particles are non-monotonic, and the extremes observed on them can exceed 100%. Moreover, the position and magnitude of the extremes strongly depend on the ellipticity of the particles, as well as on the contrast of their permittivity with the matrix.