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K0-K0bar oscillations are extremely sensitive to the K0 and K0bar energy atrest. Even assuming m_K0=m_K0bar, the energy is not granted to be the same ifgravitational effects on K0 and K0bar slightly differ. We consider variousgravitation fields present and, in particular, galactic fields, which provide anegligible acceleration, but relatively large gravitational potential energy. Aconstraint from a possible effect of this potential energy on the kaonoscillations isfound to be  |(m_g/m_i)_K0-(m_g/m_i)_K0bar| < 8 x 10^-13 atCL=90%.  The derived constraint is competitive with other tests of universality of thefree fall. Other applications are also discussed.

K0 meson physics in the gravitation field: a constraint on the equivalence principle