We discuss quantum beats in electronically excited molecular states with high rotational angular momenta J appearing in time resolved fluorescence in conditions of quadratic and linear energy shift dependence on magnetic quantum number M and external field strength. Density matrix formalism is used to obtain in explicit form the expressions for time dependent fluorescence intensity after delta-function pulsed excitation. In case of pure quadratic Stark effect, which is typical for (1) Sigma state diatomics, excited state quantum beats for J much greater than 1 exhibit a regular, or "grill" structure, consisting of narrow equidistant "principal" peaks with equal relative amplitudes on the exponential decay background. At linear polarized excitation the time intervals between the adjacent peaks are 2 pi/omega(20), omega(20) being the splitting frequency between coherently excited M-sublevels with M=2 and M’=0. If an admixture of linear contribution is present in field induced level shifts, the grill structure is superimposed by a single frequency harmonic modulation. A special geometry was found in which the quadratic beats are fully absent and the modulated grill pattern is brought into existence only by the influence of linear term. Such a case takes place when the Light polarization vector in fluorescence is directed at 45 degrees angle with respect to the exciting light polarization vector and yields the most sensitive way to separate quadratic and linear contribution. We;considered the examples when the first order term appears by a combined action of electric and magnetic field, as well as due to the e-f level electric field induced mixing, with the parameters typical for the NaK molecule.