A loop Q(·) is called a K-loop, if the identities:
        (x · y I x) · 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 IK-loop 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.