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Coherent oscillations and the evolution of the X-ray spectrum duringthermonuclear X-ray bursts in accreting neutron-star X-ray binaries have beenstudied intensively but separately. We analysed all the X-ray bursts of thesource 4U 1728-34 with the Rossi X-ray Timing Explorer. We found that thepresence of burst oscillations can be used to predict the behaviour of theblackbody radius during the cooling phase of the bursts. If a burst showsoscillations, during the cooling phase the blackbody radius remains more orless constant for ~2 - ~8s, whereas in bursts that do not show oscillations theblackbody radius either remains constant for more than ~2 - ~8s or it shows arapid (faster than ~2s) decrease and increase. Both the presence of burstoscillations and the time-dependent spectral behaviour of the bursts areaffected by accretion rate. We also found that the rise time and convexity ofthe bursts' light curve are different in bursts with and without oscillationsin 4U 1728--34. Bursts with oscillations have a short rise time (~0.5s) andshow both positive and negative convexity, whereas bursts without oscillationshave a long rise time (~1s) and mostly positive convexity. This is consistentwith the idea that burst oscillations are associated with off-equator ignition.

The link between coherent burst oscillations, burst spectral evolution and accretion state in 4U 1728-34