New uvby data collected of AN Lyn together with the reanalysis of old data establish that this star is a multiperiodic pulsator. Three independent frequencies ({nu}1=10.1756, {nu}2=18.1309 and {nu}3=9.5598c/d) and some interactions between them are found to be present in the light curve. Changes in amplitude with a large time scale are confirmed for the main frequency. Moreover, changes in amplitude are also present for the secondary frequencies, especially for {nu}3. After subtraction of the secondary frequencies from the light curves, the classical O-C method has been used to analyse the behaviour of the main period. A comparison is made between AN Lyn and the other two known {delta} Sct stars with atypical light curves, i.e., V1719 Cyg and V798 Cyg. New uvby data have been also collected for V1719 Cyg and the O-C method has been used to analyse the behaviour of the main period. It is found that the main pulsation of this star can be well described by means of a linear ephemeris with a period of P=0.26729700d over the last eighteen years. Finally, analysis of the different data sets available in the literature do not reveal significative changes in the amplitude of the main frequency of V1719 Cyg.