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).

4 pages, 5 figures, slightly revised, to appear in ApJ Letters