  We investigate the dynamical stability of the Kepler-60 planetary system with
three super-Earths. We first determine their orbital elements and masses by
Transit Timing Variation (TTV) data spanning quarters Q1-Q16 of the KEPLER
mission. The system is dynamically active but the TTV data constrain masses to
~4 Earth masses and orbits in safely wide stable zones. The observations prefer
two types of solutions. The true three-body Laplace MMR exhibits the critical
angle librating around 45 degrees and aligned apsides of the inner and outer
pair of planets. In the Laplace MMR formed through a chain of two-planet 5:4
and 4:3 MMRs, all critical angles librate with small amplitudes of ~30 degrees
and apsidal lines in planet's pairs are anti-aligned. The system is
simultaneously locked in a three-body MMR with librations amplitude of ~10
degrees. The true Laplace MMR can evolve towards a chain of two-body MMRs in
the presence of planetary migration. Therefore the three-body MMR formed in
this way seems to be more likely state of the system. However, the true
three-body MMR cannot be disregarded a priori and it remains a puzzling
configuration that may challenge the planet formation theory.
