A bidimensional vibrational Hamiltonian expressed in terms of internal coordinates has been developed to describe the symmetric stretch and the inversion of asymmetric pyramidal ammonia-like molecules. This work is an extension of the approach we have recently presented on NH3 and on some of its C-3v isotopomers [J. Chem. Phys. 115 (2001) 1243]. A new set of internal coordinates, which reflects the symmetry of the problem, has been defined and used to obtain a new bidimensional kinetic energy operator. Inversion levels for NH2D and NHD2 have been calculated variationally using an ab initio CCSD(T) bidimensional potential energy surface (PES). A good agreement with experimental values has been obtained.