  We show that in theories of generalised teleparallel gravity, whose
Lagrangians are algebraic functions of the usual teleparallel Lagrangian, the
action and the field equations are not invariant under local Lorentz
transformations. We also argue that these theories appear to have extra degrees
of freedom with respect to general relativity. The usual teleparallel
Lagrangian, which has been extensively studied and leads to a theory
dynamically equivalent to general relativity, is an exception. Both of these
facts appear to have been overlooked in the recent literature on f(T) gravity,
but are crucial for assessing the viability of these theories as alternative
explanations for the acceleration of the universe.
