We report the discovery of 20 1H/2H and 7 F/1H beat Cepheids in the SMC by the MACHO Project .
We utilize the 20 1H/2H stars to determine lightcurve shape for the SMC second-overtone ( 2H ) mode of Cepheid pulsation .
We predict , similar to the findings of Alcock et al . [ \markcite beat21997 , ApJ , submitted ] , that 2H Cepheids will have nearly or purely sinusoidal light variations ; that the P \hbox { - - } L relation for 2H Cepheids will not be distinguishable from the P \hbox { - - } L relation for 1H Cepheids within photometric accuracy ; and that 2H stars may be discernable from F and 1H stars using the amplitude-period diagram and Fourier parameter progressions for periods P \lesssim 0.7 days , our current sample 2H period limit .