  Microtubules are stiff filamentary proteins that constitute an important
component of the cytoskeleton of cells. These are known to exhibit a dynamic
instability. A steadily growing microtubule can suddenly start depolymerizing
very rapidly; this phenomenon is known as ``catastrophe''. However, often a
shrinking microtubule is ``rescued'' and starts polymerizing again. Here we
develope a model for the polymerization-depolymerization dynamics of
microtubules in the presence of {\it catastrophe-suppressing drugs}. Solving
the dynamical equations in the steady-state, we derive exact analytical
expressions for the length distributions of the microtubules tipped with
drug-bound tubulin subunits as well as those of the microtubules, in the
growing and shrinking phases, tipped with drug-free pure tubulin subunits. We
also examine the stability of the steady-state solutions.
