In precision and ultraprecision cylindrcal turning or grinding it is customary to support the workpiece with dead centres. In this paper，the effect of abnormal supporting conditions on roundness of workpiece in precision machining is discussed. Through an analysis of the relationship between the locus of the central point of the centre hole profile and frequency spectra of the out-of-roundness of centre and centre hole，the effect of geometrical deviations of centres and centre holes on roundness of workpiece the mechanism is described. An available avenue to improve the accuracy in precision and ultraprecision cylindrcal turning or grinding by centres is presented in this paper.