  The MACHO variables of LMC Field 77 that lie in the vicinity of the Cepheid
instability strip are reexamined. Among the 144 variables that we identify as
Cepheids we find 14 that have Fourier amplitudes <0.05 mag in the MACHO red
band, of which 7 have an amplitude <0.006 mag : we dub the latter group of
stars ultra-low amplitude (ULA) Cepheids. The variability of these objects is
verified by a comparison of the MACHO red with the MACHO blue lightcurves and
with those of the corresponding OGLE LMC stars. The occurrence of ULA Cepheids
is in agreement with theory. We have also discovered 2 low amplitude variables
whose periods are about a factor of 5--6 smaller than those of F Cepheids of
equal apparent magnitude. We suggest that these objects are Cepheids undergoing
pulsations in a surface mode and that they belong to a novel class of Strange
Cepheids (or Surface Mode Cepheids) whose existence was predicted by Buchler et
al. (1997).
