The propagation of coherent, polarized light in a nematic liquid crystal, governed by the nematicon equations, is considered. It is found that in the special case of 1 + 1 dimensions and the highly nonlocal limit, the nematicon equations have an asymptotic bulk solitary wave solution,termed a nematicon, whihc is given in terms of Bessel functions. This asymptotic solution gives both the ground state and the symmetric and antisymmetric excited states, which have multiple peaks. Numerical simulations of nematicon evolution, for parameters corresponding to experimental scenarios, are presented. It is found, for experimentally reasonable parameter choices, that the valitdity of the nonlocal approximation depends on the type of nematicon, as in some cases the asymptotic nematicon undergoes large amplitute oscillations. The magnitute of the nonlocality parameter for the asymptitic nematicon amplitute to be constant over a typical experimental propagation distance is also determined.