A generalization of null-spectrum for the estimation of directions of arrival of signal sources is considered. The upper and lower bounds of a class of the generalized null-spectrum, the maximum and minimum null-spectra, are derived. The authors observe that the maximum null-spectrum has higher resolution capability than other null-spectra including the multiple signal classification and Min-Norm null-spectra. In addition, it is seen that the estimates of the direction of arrival obtained by using the maximum and multiple signal classification null-spectra have the same asymptotic distribution. Through computer simulation the probabilities of resolution of various null-spectra are obtained, from which they confirmed the resolution capability of the maximum null-spectrum.