The perception of externalization of speech sounds was investigated with respect to the monaural and binaural cues available at the listeners' ears in a reverberant environment. Individualized binaural room impulse responses (BRIRs) were used to simulate externalized sound sources via headphones. The measured BRIRs were subsequently modified such that the proportion of the response containing binaural vs monaural information was varied. Normal-hearing listeners were presented with speech sounds convolved with such modified BRIRs. Monaural reverberation cues were found to be sufficient for the externalization of a lateral sound source. In contrast, for a frontal source, an increased amount of binaural cues from reflections was required in order to obtain well externalized sound images. It was demonstrated that the interaction between the interaural cues of the direct sound and the reverberation strongly affects the perception of externalization. An analysis of the short-term binaural cues showed that the amount of fluctuations of the binaural cues corresponded well to the externalization ratings obtained in the listening tests. The results further suggested that the precedence effect is involved in the auditory processing of the dynamic binaural cues that are utilized for externalization perception.