  We elucidate the properties of mixed-gap vector surface solitons supported by
the interface between a uniform medium and an optical lattice imprinted in a
Kerr-type nonlinear media. The components of such mixed-gap solitons emerge
from different gaps of lattice spectrum and their mutual trapping results in
the formation of stable vector states. The unstable soliton component is
stabilized by the cross-coupling with the stable component. We show that vector
mixed-gap surface solitons exhibit a new combination of properties of vectorial
surface waves and gap solitons.
