  Aims: Our goal was to increase number of known doubly eclipsing systems such
that the resulting dataset would allow to study them via statistical means, as
well as prove that they constitute gravitationally bound 2+2 quadruple system.
Methods: We analysed photometric data for eclipsing binaries provided by the
OGLE survey in the LMC fields. We found a large number of new doubly eclipsing
systems (our discoveries are 3x more numerous than previous studies). With a
typical orbital period of days for the binaries, we sought eclipse time
variations (ETVs) on the timescale of years. In the cases where we were able to
detect the ETV period, the difference between the inner and outer periods in
the quadruple system is large enough. This allows us to interpret ETVs
primarily as the light-time effect, thus providing an interesting constraint on
masses of the binaries. Results: In addition to significantly enlarging the
database of known doubly eclipsing systems, we performed a thorough analysis of
72 cases. ETVs for 28 of them (39% of the studied cases) showed evidence of
relative motion. We note OGLE BLG-ECL-145467 as the most interesting case; it
is bright (I=12.6 mag), consists of two detached binaries with periods of about
3.3 d and 4.9 d (making it a candidate for a 3:2 resonant system), mutual
period about 1538 d. Distribution of the orbital period ratio P_A/P_B of
binaries in 2+2 quadruples shows statistically significant excess at 1 and 1.5.
The former is likely a natural statistical preference in weakly interacting
systems with periods within the same range. The latter is thought to be
evidence of a capture in the 3:2 mean motion resonance of the two binaries.
This sets important constraints on evolutionary channels in these systems. The
total number of doubly eclipsing systems increased to 146, more than 90% of
which are at low declinations on the southern sky.
