  MACHO Project photometry of 45 LMC FO/SO beat Cepheids which pulsate in the
first and second overtone (FO and SOo, respectively) has been analysed to
determine the lightcurve characteristics for the SO mode of Cepheid pulsation.
We predict that singly-periodic SO Cepheids will have nearly sinusoidal
lightcurves; that we will only be able to discern SO Cepheids from fundamental
(F) and (FO) Cepheids for P <= 1.4 days; and that the SO distribution will
overlap the short-period edge of the LMC FO Cepheid period-luminosity relation
(when both are plotted as a function of photometric period).
  We also report the discovery of one SO Cepheid candidate,
MACHO*05:03:39.6$-$70:04:32, with a photometric period of 0.775961 +/- 0.000019
days and an instrumental amplitude of 0.047 +/- 0.009 mag in V.
