Existence of subsonic second slip waves, a variant of interfacial (Sto
neley) waves, is investigated using the Stroh sextic formalism. We hav
e examined the second slip wave propagating along an interface between
two identical half-infinite anisotropic media which have the same ori
entation. Special attention is paid to exceptional transonic states wh
ere the appearance of a certain bulk wave may prevent the existence of
the second slip wave. By examining the impedance tensor at various tr
ansonic states, we formulate an existence theorem for second slip wave
s. Numerical examples are shown for materials with various symmetries,
which give convincing evidence for the existence of second slip waves
.