The influence of the spectral bandwidth of the spectrometer on the performance of the spectrometer is of great importance in atomic absorption spectrometry using continuum source (CS-AAS). For a theoretical analysis of the detection of small absorbances two cases have to be taken into account: as long as the limiting noise of the signal is given by the detector noise an increase in spectral bandwidth of the spectrometer implies an improvement in the limit of detection. In contrast, if the noise of the signal is dominated by the photon shot noise the detection limit should become independent of the spectral bandwidth. In this case the spectral bandwidth of the spectrometer should be chosen equal to the bandwidth of the absorption line to avoid spectral interferences. Theoretical calculations are presented for the dependence of the characteristic mass on the spectral bandwidth in case of CS-AAS measurements. The results are compared with experimental measurements for six different elements using continuum source as well as line sources. The investigations were done using a double echelle monochromator (DEMON) which offers a high spectral resolution lambda/Deltalambda of about 140,000.