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Given two non-weakly k-normal Boolean functions on n variables a method is proposed to construct a non-weakly (k + 1)-normal Boolean function on (n + 2)-variables.

It is proved that no non-quadratic Kasami bent is affine equivalent to Maiorana-MacFarland type bent functions.

Given two non-weakly k-normal Boolean functions on n-variables a method is proposed to construct a non-weakly (k + 1)-normal Boolean function on (n + 2)-variables.

A new invariant of the set of n-variable Boolean functions with respect to the action of AGL(n, 2) is studied. Application of this invariant to prove affine nonequiv-alence of two Boolean functions is outlined. The value of this invariant is computed for P S ap type bent functions.

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