  We begin the study of the spectrum of BPS branes and its variation on lines
of marginal stability on O_P^2(-3), a Calabi-Yau ALE space asymptotic to
C^3/Z_3. We show how to get the complete spectrum near the large volume limit
and near the orbifold point, and find a striking similarity between the
descriptions of holomorphic bundles and BPS branes in these two limits. We use
these results to develop a general picture of the spectrum. We also suggest a
generalization of some of the ideas to the quintic Calabi-Yau.
