  We consider the effects of mutual transits by extrasolar planet-companion
systems (in a true binary or a planet-satellite system) on light curves. We
show that induced changes in light curves depend strongly on a ratio between a
planet-companion's orbital velocity around their host star and a
planet-companion's spin speed around their common center of mass. In both the
slow and fast spin cases (corresponding to long and short distances between
them, respectively), a certain asymmetry appears in light curves. We show that,
especially in the case of short distances, occultation of one faint object by
the other, while the transit of the planet-companion system occurs in front of
its parent star, causes an apparent increase in light curves and characteristic
fluctuations appear as important evidence of mutual transits. We show also that
extrasolar mutual transits provide a complementary method of measuring the
radii of two transiting objects, their separation and mass, and consequently
identifying them as a true binary, planet-satellite system or others.
Monitoring $10^5$ stars for three years with Kepler may lead to a discovery of
a second Earth-Moon-like system if the fraction of such systems for an averaged
star is larger than 0.05, or it may put upper limits on the fraction as f <
0.05.
