  We have analysed the photometry of 924 type II Cepheids from the Galactic
bulge observed by the Optical Gravitational Lensing Experiment. Our goal was to
detect and analyse various dynamical phenomena, including, e.g. multi-mode
pulsation, period-doubled pulsation, period-k pulsation, or quasi-periodic
modulation of pulsation. First examples of double-mode BL Her-type stars,
pulsating simultaneously in the fundamental and first overtone modes are
reported. Two double-mode pulsators are not isolated cases however, but form an
extension of recently identified class of long-period RRd stars. Period
doubling effect was detected in three BL Her-type stars: two were identified
previously and one is a new discovery. Through identification of numerous
period-doubled W Vir stars we show that the appearance of the period doubling
effect, and hence the transition towards RV Tau class, is a smooth process that
starts at pulsation periods slightly above 15d. Interchange of the deep and
shallow pulsation cycles is identified in tens of RV Tau variables. One RV Tau
star is a strong candidate for period-4 pulsation. Quasi-periodic modulation of
pulsation in all sub-classes of type II Cepheids is reported for the first
time. Modulation was detected in 16 BL Her, 9 W Vir and in 7 RV Tau stars. In
the last case, modulation is the most likely scenario, but two other scenarios,
excitation of non-radial modes, or period-4 pulsation, can also account for the
observed pulsation pattern. Irregular changes of pulsation amplitude and period
on various time-scales are common in all subgroups of type II Cepheids.
