In this paper we report the results of simultaneous observations, using rapid continuous differential photometry, of the δ Scuti star 63 Her and of a normal main sequence F2V star, HD 155543. These observations, which lasted three weeks, in May-June 1987, were performed at the 1.5 m telescopes of the "Observatorio del Teide", in Tenerife (Spain), and of the "observatorio Astronómico Nacional de San Pedro Martir", in Baja California (Mexico), both equipped with identical three channel photometers. As usual, the main limitations for detection of oscillations are due to atmospheric noise, and aliases due to the observing window. In the range 0.5 to 5 mHz, the noise level which was achieved was of the order of 8 μmag per independent frequency. Six frequencies of pulsation have been unambiguously detected for 63 Her in the range 0.04-0.30 mHz; the spectral peak at 0.131 mHz corresponds to the fundamental radial mode of a star occupying the same place as 63 Her in the HR diagram. Three detected frequencies are smaller than 0.131 mHz, suggesting that gravity modes have been observed for this star. There is some evidence for detection of oscillations in the F2V star, whose detailed analysis has been presented in another paper.