  For a continuous curve of families of Dirac type operators we define a higher
spectral flow as a $K$-group element. We show that this higher spectral flow
can be computed analytically by $\heta$-forms, and is related to the family
index in the same way as the spectral flow is related to the index. We
introduce a notion of Toeplitz family and relate its index to the higher
spectral flow. Applications to family indices for manifolds with boundary are
also given.
