We report the results of the CPLEAR experiment on CP-, T- and CPT-symmetries in the neutral kaon system. CP-violation parameters are given for different decay channels. For the first time T-violation is measured by a direct method using semileptonic decays. The CPT symmetry in the kaons decays is tested through the parameters Im( δ ), from the Bell-Steinberger relation, with a precision of 10 −5 and Re( δ ) with a precision of a few 10 −4 (two order of magnitude better than the previous measurement). These two measurements allow us to bound the difference in mass and width of K 0 and ¯K 0 to be equal within 10 −18 GeV. In the limit of CPT invariance in the neutral kaon decays, the K 0 and ¯K 0 masses are equal within 10 −19 GeV.