We present the results of the deterministic identifiability analysis based on similarity transformation for models of one-state excited-state events of cylindrically symmetric rotors in isotropic environments undergoing rotational diffusion described by Brownian reorientation. Such an analysis on error-free time-resolved fluorescence (anisotropy) data can reveal whether the parameters of the considered model can be determined. The fluorescence delta-response functions I-parallel to (t) and I-perpendicular to(t), for fluorescence polarized respectively parallel and perpendicular to the electric vector of linearly polarized excitation, are used to construct, in convenient matrix form, expressions of the sum S(t)=I-parallel to(t)+2I(perpendicular to)(t), the difference D(t)=I-parallel to(t)-I-perpendicular to(t), and the time-resolved fluorescence anisotropy r(t)=D(t)/S(t). The identiflability analysis of r(t) demonstrates that the rotational diffusion coefficients D-parallel to and D-perpendicular to for rotation respectively about and perpendicular to the symmetry axis can be uniquely resolved. However, the polar and azimuthal angles defining the absorption and emission transition moments in the molecular reference frame are not individually identifiable. Nevertheless, the difference between the polar angles of these transition moments is uniquely determined.