We study cosmological perturbations for k-essence and kinetic gravity
braiding models in the context of the two-field measure theory (TMT).
Considering scalar perturbations and the uniform field gauge, we obtain the
sound speed of the fields and present a stability analysis by means of the
kinetic matrix and the mass eigenvalues. For k-essence models, in the two-field
measure theory, the speed of propagation of the field is modified completely
due to the new measure field and it gives rise to crucial differences with
respect to the case without new measure. The stability analysis gives a
physical viable model for the Universe. For the kinetic gravity braiding models
in the two-field measure theory we get that, in general, the speed of
perturbations is equal to the speed of light which is a consequence of the
properties of the new measure field. In the later case, there is always a ghost
field. Furthermore, we calculate general expressions for the mass eigenvalues
and find, for an explicit example, the existence of tachyonic instabilities.