We report the results of the CPLEAR experiment on CP-, T- and CPT-symmetrie
s in the neutral kaon system. CP-violation parameters are given for differe
nt decay channels. For the first time T-violation is measured by a direct m
ethod using semileptonic decays. The CPT symmetry in the kaons decays is te
sted through the parameters Im(delta), from the Bell-Steinberger relation,
with a precision. of 10(-5) and Re(delta) with a precision of a. few 10(-4)
(two order of magnitude better than the previous measurement). These two m
easurements allow us to bound the difference in mass and width of K-0 and (
K) over bar(0) It to be equal within 10(-18) GeV. In the limit of CPT invar
iance in the neutral kaon decays, the K-0 and (K) over bar(0) masses are eq
ual within 10(-19) GeV.