  We present detailed NLTE Ti~I calculations in model atmospheres of cool dwarf
and giant stars. A fully self-consistent NLTE treatment for a Ti~I model atom
with 395 levels and 5279 primary bound-bound transitions is included, and we
discuss the implication of departures from LTE in this atom for the strengths
of Ti~I lines and TiO molecular bands in cool star spectra. We show that in the
atmospheric parameter range investigated, LTE is a poor approximation to Ti~I
line formation, as expected from the low collisional rates in cool stars. The
secondary effects of Ti~I overionization on the TiO number density and the TiO
molecular opacities, however, are found to be negligible in the molecular line
forming region for the relatively small parameter range studied in this paper.
