Many industrial applications of high-power lasers involve the creation by vaporization of a keyhole in a solid target. This structure is unstable with respect to collapse and can be maintained only by achieving a balance between pressure terms from laser vaporization and those of surface tension and hydrostatics. In addition, liquid flow and plasma effects also modulate the laser beam intensity resulting in a complex feedback system in coupling laser radiation into the target. In this paper, we report data obtained on the time dependence of structures associated with laser drilling of an absorbing liquid. These data, obtained at low incident laser intensities in the absence of plasma effects, show the complex nature of the laser-keyhole interaction even in a two-phase system. Some results of experiments carried out in low gravity are also presented.