  We perform a Next-to-Leading order analysis of Delta S=2 processes beyond the
Standard Model. Combining the recently computed NLO anomalous dimensions and
the B parameters of the most general Delta S=2 effective Hamiltonian, we give
an analytic formula for Delta M_K and epsilon_K in terms of the Wilson
coefficients at the high energy scale. This expression can be used for any
extension of the Standard Model with new heavy particles. Using this result, we
consider gluino-mediated contributions to Delta S=2 transitions in general SUSY
models and provide an improved analysis of the constraints on off-diagonal mass
terms between the first two generations of down-type squarks. Finally, we
improve the constraints on R-violating couplings from Delta M_K and epsilon_K.
