The Kolmogorov decomposition of positive definite kernels in context of Hilbert C^*-modules was given by G. J. Murphy [Proc. Edinburgh Math. Soc. (2) 40 (1997), no. 2, 367--374]. In this talk, we investigate positive definite and conditionally positive definite kernels in the context of Hilbert C^*-modules and give a characterizati on of the conditionally positive definiteness in terms of the usual positive definiteness. In addition, we present a Kolmogorov type representation of conditionally positive definite kernels in the setting of Hilbert C^*-modules and give a characterization of the order K'\leq K between conditionally positive definite kernels.

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