Summary: Given a vector bundle \(V\) of rank \(n\) on a variety \(X\), together with two complete flags of subbundles, there is a degeneracy locus \(X_w\subset X\) for each \(w\) in the symmetric group \(S_n\). With suitable genericity hypotheses, the class of \(X_w\) in the Chow group of \(X\) is given by a double Schubert polynomial in the first Chern classes of the quotient line bundles of the flags [W. Fulton, Duke Math. J. 65, No. 3, 381-420 (1992; Zbl 0788.14044)]. In this note we give similar formulas for corresponding loci when \(V\) has an orthogonal or symplectic structure and the flags are isotropic; there is one such locus \(X_w\) for each \(w\) in the corresponding Weyl group.