Properties of (skew-symmetric) conformal Yano-Killing tensors are reviewed. Explicit forms of three symmetric conformal Killing tensors in Kerr spacetime are obtained from the Yano-Killing tensor. The relation between spin-2 fields and solutions to the Maxwell equations is used in the construction of a new conserved quantity which is quadratic in terms of the Weyl tensor. The formula obtained is similar to the functional obtained from the Bel-Robinson tensor and is examined in Kerr spacetime. A new interpretation of the conserved quantity obtained is proposed. * Partially supported by grants KBN 2 P03B 073 24 and EPSRC: EP/D032091/1. which are simple consequences of the definition (1.1) and spin-2 field properties (cf. Definition 4 below). A contraction of T gives the Bel-Robinson tensor:Moreover, in [28] the following propertiesof the tensor T are shown. They enable one to formulate the following Theorem 1. If P, Q are CYK tensors, X is a conformal vector field and T obeys the properties (1.2) and (1.3) then

Symmetric conformal Killing tensors and (skew-symmetric) conformal YanoKilling tensors for Euclidean Taub-NUT metric are given in explicit form. Relations between Yano and CYK tensors in terms of conformal rescaling are discussed.

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