  We employ the very recent photometric data of the OGLE project together with
stellar atmosphere and linear pulsation models to determine the distance
modulus of the Small Magellanic Cloud from its double-mode Cepheids. Based on
the requirement of obtaining the same distance modulus DM from the two types of
variables (fundamental & first overtone and first & second overtone), we get
DM=19.05 mag, with a very small statistical error (standard deviation) of 0.017
mag. Various systematic and zero point ambiguities (primarily those of the
color - temperature transformation) lead to an error of +/-0.13 mag (estimated
3 sigma deviation). This result is in very good agreement with the distance
modulus of the Large Magellanic Cloud of 18.5 mag, derived earlier from cluster
double-mode RR Lyrae stars.
