A loop Q(¢) is called a K-loop, if the identities: (x ¢ yIx) ¢ xz = x ¢ yz ; (y ¢ x) ¢ (I¡1xz ¢ x) = yz ¢ x ( Ix = x¡1 ; I¡1x = ¡1x ; I¡1x ¢ z = ¡1x ¢ z ) hold. A K-loop is called an IK-loop if the substitution I is an automorphism of the loop. It is proved that: a K-loop generated by one element is solvable; in a IKloop the center Z(Q) and the nucleus N coincide and every IK-loop is nilpotent. Examples of K-loops, generated by one element are given.