The experiment reported here examines the relationship between the perceptual organisation of the simultaneous frequency components of a complex tone, and the illusion of continuity that is experienced when a tone alternates with a sufficiently intense noise. Are the conditions for illusory continuity determined by processes that are entirely local in frequency, or are judgments of continuity made on auditory objects, whose composition is determined by grouping rules that extend widely over different frequency components? Listeners made continuous / pulsating judgments on a variety of complex tones that repeatedly alternated with a 100-500-Hz bandpass noise. A Dull complex tone consisting of the first three harmonics of 140 Hz was heard as continuous when its energy was lower than that of the noise. Adding three higher harmonics to this complex produced a Rich tone that did not appear continuous even at low levels. However, mistuning these added higher harmonics produced a Mixed percept of two different-pitched tones, one similar to the original Dull tone which was heard as continuous at low levels, and one thin tone corresponding to the mistuned higher harmonics which continued to pulsate. After exposure to this Mixed sound, listeners were more likely to hear-out and make continuous the lower harmonics of the Rich sound. The experiment demonstrates that judgments of auditory continuity are based on entire simultaneously-grouped objects rather than being determined locally by individual frequency-channel.