The brightness variability of 12 stars of spectral class A which are type ROTD objects is analyzed. The power spectra of these objects contain characteristic features including a amplitude-dominant narrow peak at a frequency F1(phot) as well as at lower frequencies, a broad peak that generally is made up of numerous components. In power spectra constructed from each of sets of observations lasting 90 days, the peak at F1(phot) is present in most of the diagrams, but it is not always the highest in amplitude. It is concluded that the peak at F1(phot) predominates since it is present in the periodograms for every set of observations, while the positions and amplitudes of the other peaks vary and, therefore, form a set of peaks with lower amplitudes in the resulting periodogram. Indications are obtained of rather rapid evolution of structures on the surface of ROTD stars on the order of the 90 day duration of the a of observations. These may be Rossby waves or spots if the traditional interpretation is sustained. Assuming that differential rotation is present in most of these stars, values of the parameter ΔΩ have been found for the 12 ROTD stars and compared with published data. Our measurements confirm that ΔΩ is considerably higher in the stars hotter than 6700 K. The average measured value of ΔΩ for the 12 ROTD stars we have studied is 0.61±0.10 rad/day and is in good agreement with the literature. Theoretical studies allow a significant value of ΔΩ for stars in spectral classes A-F. The possibility that the peaks appear in the power spectrum because of differential rotation of a star with spots cannot be excluded.