  In a number of recent experiments with microwave high quality superconducting
coplanar waveguide (CPW) resonators an anomalously weak power dependence of the
quality factor has been observed. We argue that this observation implies that
the monochromatic radiation does not saturate the Two Level Systems (TLS)
located at the interface oxide surfaces of the resonator and suggests the
importance of their interactions. We estimate the microwave loss due to
interacting TLS and show that the interactions between TLS lead to a drift of
their energies that result in a much slower, logarithmic dependence of their
absorption on the radiation power in agreement with the data.
