Extended empirical orthogonal functions (EOFs) are used to define a phase space for the analysis of tropical stratospheric wind data, extending our previous study of the quasi-biennial oscillation (QBO) in several manners. First, the sensitivity of the analysis to the length of the window (w) is discussed in some detail. As w increases, the leading pair of EOFs become more concentrated on the period near 28 months; simultaneously, the signals contained in higher-order EOFs become more significant, with more clearly defined periodicities; however, for large w more EOFs are required to represent the same variance. There appear to be two stable regimes: when w is less than 20 months the first two EOFs describe a QBO with some irregularities in the onset of easterly wind regimes, whereas when w exceeds 30 months such irregularities are represented by the third and fourth EOFS. Second, the first pair of EOFs with w = 40 are regarded as representing a pure QBO signal, subject to variations in cycle length (ranging from 22 to 33 months) and amplitude but propagating smoothly. Its phase–space characteristics are examined in some detail; this oscillation is regarded as a limit cycle, subject to low-frequency variability, presumably due to fluctuations in the forcing mechanisms at work. No annual cycle is evident in its propagation in phase space. Third, departures from this pure QBO are examined. These are represented by higher-order signals with w = 40. EOFs 3 and 4 describe much of the irregularity in downward propagation of the wind regimes, with dominant periods in a broad band centered on 28 months; EOF 5 does not represent a propagating signal but some low-frequency variability (probably externally forced) in the vertical wind shear; E0Fs 6 and 7 are the subharmonics of the QBO; EOFs 8 and 9 represent the annual cycle.