he aim of NML is to approximate the kinetics or thermodynamics of a biomolecule by a reduced model based on a normal mode decomposition of the dynamical space. Our basis set uses the eigenvectors of a mass re-weighted Hessian matrix calculated with a biomolecular force field. Low frequency eigenvalues correspond to more collective motions, whereas the highest frequency eigenvalues are the limiting factor for the stability of the integrator. The higher frequency modes are overdamped and relaxed near to their energy minimum while respecting the subspace of low frequency dynamical modes. Numerical results confirm that both sampling and rates are conserved for an implicitly solvated alanine dipeptide model, with only 30% of the modes propagated, when compared to the full model. For implicitly solvated systems the method can be shown to give improvements in efficiency more than 2 times even for sampling a small 22 atom (alanine dipeptide) model and in excess of an order of magnitude for sampling an 882 atom (bovine pancreatic trypsin inhibitor, or BPTI) model, with good scaling with system size subject to the number of modes propagated.