The generalized expressions of the measurable CP violating parameters for the K system are given, without assuming CPTinvariance or the other usual assumptions such as: dQ = -AS, the approximate AZ = $ rule. The unitarity sum rule for the K" decays is also studied without using these assumptions. Some applications of these generalized expressions are discussed. We suggest a test for CPT invariance by testing an inequality between the charge asymmetries of KL '-f rev(&) and KL -+ v&R,). Using the upper bound on the e -p asymmetry for the K* decays, we show that any signitlcant difference between R, and R, indicates some CPT violation. Alternatively, even a small e -p asymmetry may lead to considerably different R,,,, , if CPTis violated. As another application we construct a CPT violating phenomenological model, in which there is no mass or lifetime difference between particles and their antiparticles even in the presence of CPT violation. We give also the "second-order" corrections to the phases of c and 8 in the case of CPT and T invariance, respectively. It is found that according to the available experimental results 4, should be considerably lower than 43".