In this study, we describe the results of ab initio (HF and MP2) and MNDO-PM3 calculations on the model reactions of unstabilized (Me3P=CH-CH3), semistabilized (Me3P=CH-C=CH), and stabilized (Me3P=CH-C=N) ylides with acetaldehyde to form their respective Z and E olefins and trimethylphosphine oxide. These reactions occur in three stages: oxaphosphetane formation, oxaphosphetane pseudorotation, and oxaphosphetane decomposition. The calculated barriers for these processes vary considerably depending on the level of theory employed (ab initio vs. MNDO-PM3 or HF vs. MP2 at the ab initio level). However, self-consistent geometries of reactants, intermediates, transition states and products are obtained at all levels. Oxaphosphetane formation is best described as very asynchronous cycloaddition (borderline two-step mechanisms). The geometries of the transition states are near planar with respect to P, C, C, and O atoms. Analysis of the bond indices of these reactions shows that the C-C bonds are between 44% (unstabilized case) and 60% (stabilized case) formed whereas the corresponding P-O bonds have not been formed to any significant degree. Oxaphosphetane decomposition can be described as a very asynchronous retrocycloaddition where P-C bond breakage runs ahead of C-O bond breakage. These results are compared with experimental findings for the Wittig reaction, and its relevance to the overall mechanism of the olefination is discussed. (C) 1997 John Wiley & Sons, Inc.