The problem of adaptive control of discrete or continuous linear scalar objects is examined. The control object parameters are unknown. The locations of the zeros of the numerator of the control-to-observed output transfer function are arbitrary, but they must not coincide with the denominator zeros. The object is subject to a nonmeasured bounded perturbation. The control acts on the object with a constant, but unknown, lag. It is guaranteed that, after the termination of the transient processes, the deviation of the observed output from the desired zero value does not exceed a constant value that is proportional to the amplitude of the perturbation.