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Using raising operators and geometric arguments, we establish formulas forthe K-theory classes of degeneracy loci in classical types. We also find newdeterminantal and Pfaffian expressions for classical cases considered byGiambelli: the loci where a generic matrix drops rank, and where a genericsymmetric or skew-symmetric matrix drops rank.  In an appendix, we construct a K-theoretic Euler class for even-rank vectorbundles with quadratic form, refining the Chow-theoretic class introduced byEdidin and Graham. We also establish a relation between top Chern classes ofmaximal isotropic subbundles, which is used in proving the type D degeneracylocus formulas.

K-theoretic Chern class formulas for vexillary degeneracy loci