This paper undertakes the investigation of the disposition to stress of Nigerian users of English and the nature of spoken Nigerian English rhythm. The subjects of the study were sixty Nigerians of varied socio-economic, educational and ethno-linguistic backgrounds and a native (British) English speaker, whose productions from reading a passage and speaking freely for three minutes on a common topic were analysed metrically, acoustically and statistically, using a modified version of the Metrical Theory, the Wilcoxon Matched Pairs Signed Ranks Test and the Analysis of Variance (ANOVA). In spite of earlier classifications, the study assumes the existence of three varieties of spoken Nigerian English characterized by their disposition to stress and speech rhythm: the "Non-Standard", the "Standard" and the "Sophisticated" varieties, which are individually different but collectively similar yet different from Standard British English, represented by the control's performance. The existence of the three varieties is confirmed by the data. The common performance features include a tendency to stress more syllables in words than the native speaker. This feature, which is traceable to the influence of the syllable-timing rhythm of the subjects' mother tongues, tends to characterize the Nigerian accent of English; but whereas the Non-Standard Variety conforms to the syllable-timing description the Standard and Sophisticated Varieties require further investigation.