  A nonlinear kinetic chemotaxis model with internal dynamics incorporating
signal transduction and adaptation is considered. This paper is concerned with:
(i) the global solution for this model, and, (ii) its fast adaptation limit to
Othmer-Dunbar-Alt type model. This limit gives some insight to the molecular
origin of the chemotaxis behaviour.
  First, by using the Schauder fixed point theorem, the global existence of
weak solution is proved based on detailed a priori estimates, under some quite
general assumptions on the model and the initial data. However, the Schauder
fixed point theorem does not provide uniqueness. Therefore, additional analysis
is required to be developed to obtain uniqueness.
  Next, the fast adaptation limit of this model is derived by extracting a weak
convergence subsequence in measure space. For this limit, the first difficulty
is to show the concentration effect on the internal state. When the small
parameter {\epsilon}, the adaptation time scale, goes to zero, we prove that
the solution converges to a Dirac mass in the internal state variable. Another
difficulty is the strong compactness argument on the chemical potential, which
is essential for passing the nonlinear kinetic equation to the weak limit.
