We examine the properties of 17 long period (80-180 days) and very luminous
(median absolute magnitude of M_I= -7.93 and M_V= -7.03) Cepheids to see if
they can serve as an useful distance indicator. We find that these Ultra Long
Period (ULP) Cepheids have a relatively shallow Period-Luminosity (PL)
relation, so in fact they are more "standard candle"-like than classical
Cepheids. In the reddening-free Wesenheit index, the slope of the ULP PL
relation is ~10 times less steep than the standard PL relation for the SMC
Cepheids. The scatter of our sample about the W_I PL relation is 0.22 mag,
approaching that of classical Cepheids and Type Ia Supernovae. We expect this
scatter to decrease as bigger and more uniform samples of ULP Cepheids are
obtained. We also measure a non-zero period derivative for one ULP Cepheid (SMC
HV829) and use the result to probe evolutionary models and mass loss of massive
stars. ULP Cepheids main advantage over classical Cepheids is that they are
more luminous, and as such show great potential as stellar distance indicators
to galaxies up to 100 Mpc and beyond.Comment: Accepted for Publication in ApJ. 11 pages, 8 figure