Polycrystalline and mosaic bicrystalline titanium films were subjected to steep heating/cooling rate of 1011/108 K s-1 by laser pulsing. The induced phase transformations were followed by imaging and diffraction with a dynamic transmission electron microscope on the time scale of nanoseconds. On heating the film up to near the melting point with a 6-ns laser pulse, the low-temperature hcp phase transformed to the high-temperature bcc phase, with a nucleation rate of 1025 m-3 s-1 and a crystal-growth velocity of about 1000 m s-1. Quenching of molten Ti first produced the bcc phase, which in turn transformed to the hcp phase within a few microseconds. Thus, hcp-bcc transformations occur in Ti, even at the above high thermal rates. They are martensitic and not diffusion limited as claimed for transformations at low thermal rates. [ABSTRACT FROM AUTHOR]