  We define the wonderful compactification of an arrangement of subvarieties.
Given a complex nonsingular algebraic variety $Y$ and certain collection
$\mathcal{G}$ of subvarieties of $Y$, the wonderful compactification
$Y_\mathcal{G}$ can be constructed by a sequence of blow-ups of $Y$ along the
subvarieties of the arrangement. This generalizes the Fulton-MacPherson
configuration spaces and the wonderful models given by De Concini and Procesi.
  We give a condition on the order of blow-ups in the construction of
$Y_\mathcal{G}$ such that each blow-up is along a nonsingular center.
