  Searches for lepton flavour and lepton number violation in kaon decays by the
NA48/2 and NA62 experiments at CERN are presented. A precision measurement of
the helicity-suppressed ratio RK of the K --> e nu and K --> mu nu decay rates
has been performed using the full data set collected by the NA62 collaboration
in 2007. The data sample amounted to 145,958 reconstructed K --> e nu
candidates with 11.0% background contamination. The result is RK = (2.488 +-
0.010) X 10^{-5}, which is in agreement with the Standard Model expectation. An
improved upper limit on the lepton number violating K+- --> pi-+ mu+- mu+-
decay rate is also presented.
