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We have analysed the photometry of 924 type II Cepheids from the Galacticbulge observed by the Optical Gravitational Lensing Experiment. Our goal was todetect and analyse various dynamical phenomena, including, e.g. multi-modepulsation, period-doubled pulsation, period-k pulsation, or quasi-periodicmodulation of pulsation. First examples of double-mode BL Her-type stars,pulsating simultaneously in the fundamental and first overtone modes arereported. Two double-mode pulsators are not isolated cases however, but form anextension of recently identified class of long-period RRd stars. Perioddoubling effect was detected in three BL Her-type stars: two were identifiedpreviously and one is a new discovery. Through identification of numerousperiod-doubled W Vir stars we show that the appearance of the period doublingeffect, and hence the transition towards RV Tau class, is a smooth process thatstarts at pulsation periods slightly above 15d. Interchange of the deep andshallow pulsation cycles is identified in tens of RV Tau variables. One RV Taustar is a strong candidate for period-4 pulsation. Quasi-periodic modulation ofpulsation in all sub-classes of type II Cepheids is reported for the firsttime. Modulation was detected in 16 BL Her, 9 W Vir and in 7 RV Tau stars. Inthe 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 theobserved pulsation pattern. Irregular changes of pulsation amplitude and periodon various time-scales are common in all subgroups of type II Cepheids.

Diversity of dynamical phenomena in type II Cepheids of the OGLE collection