  We propose a theory of double Schubert polynomials P_w(X,Y) for the Lie types
B, C, D which naturally extends the family of Lascoux of Schutzenberger in type
A. These polynomials satisfy positivity, orthogonality, and stability
properties, and represent the classes of Schubert varieties and degeneracy loci
of vector bundles. When w is a maximal Grassmannian element of the Weyl group,
P_w(X,Y) can be expressed in terms of Schur-type determinants and Pfaffians, in
analogy with the type A formula of Kempf and Laksov. An example, motivated by
quantum cohomology, shows that there are no Chern class formulas for degeneracy
loci of ``isotropic morphisms'' of bundles.
