  We show that, at the classical level, the recently proposed `ambitwistor
string' model is equivalent to the spinor moving frame formulation of
null-supersting, which in its turn is equivalent to Siegel's formulation of
closed twistor string or to its higher dimensional generalizations. Although
the null-(super)string is usually considered as describing the tensionless
limit of (super)string, we show that its action can be derived from the spinor
moving frame formulation of superstring also in the infinite tension limit.
This observation allows us to argue on the absence of critical dimensions and
suggests that the (ambi)twistor string based technique(s) to calculate field
theory amplitudes can be developed not only in D=10 or 26, but also in D=11 and
other dimensions. The D=11 and D=10 twistor strings are described in some
details.
