The authors measure the time-dependent CP asymmetry parameters in B{sup 0} {yields} K{sup +}K{sup -}K{sup 0} based on a data sample of approximately 277 million B-meson pairs recorded at the {Upsilon}(4S) resonance with the BABAR detector at the PEP-II B-meson Factory at SLAC. They reconstruct two-body B{sup 0} decays to {phi}(1020)K{sub s}{sup 0} and {phi}(1020)K{sub L}{sup 0}. Using a time-dependent maximum-likelihood fit, they measure sin2{beta}{sub eff}({phi}K{sup 0}) = 0.48 {+-} 0.28 {+-} 0.10, and C({phi}K{sup 0}) = 0.16 {+-} 0.25 {+-} 0.09, where the first error is statistical, and the second is systematic. They also present measurements of the CP-violating asymmetries in the decay B{sup 0} {yields} f{sub 0}({yields} {pi}{sup +}{pi}{sup -})K{sub s}{sup 0}. The results are obtained from a data sample of 209 x 10{sup 6} {Upsilon}(4S) {yields} B{bar B} decays, also collected with the BABAR detector at the PEP-II asymmetric-energy B Factory at SLAC. From a time-dependent maximum-likelihood fit they measure the mixing-induced CP violation parameter S(f{sub 0}(980)K{sub S}{sup 0}) = - sin 2{beta}{sub eff}f{sub 0}(980)K{sub S}{sup 0} = -0.95{sub -0.23}{sup +0.32} {+-} 0.10 and the direct CP violation parameter C(f{sub 0}(980)K{sub S}{sup 0}) = - 0.24 {+-} 0.31 {+-} 0.15, where the first errors are statistical and …