A class of adaptive bi-iteration SVD (Bi-SVD) algorithms for tracking structured subspaces of the form E_=[E E/spl Psi//sub 1/ E/spl Psi//sub 2/... E/spl Psi//sub n-1/] is introduced, where E is an N/spl times/r, N/spl ges/r orthonormal core basis matrix, and /spl Psi//sub 1/, /spl Psi//sub 2/, ..., /spl Psi//sub n-1/ is a set of r/spl times/r subrotors. Structured subspaces of this kind arise in all forms of multiple invariance (MI) techniques, such as MI-ESPRIT. An adaptive MI-ESPRIT algorithm using Bi-SVD MI subspace tracking is developed. Computer experiments validate the theoretical results.