NTM's and the halting problem
A nondeterministic Turing machine can be simulated using a deterministic Turing machine in exponential time (can be shown as a simple exercise). Furthermore, NDTM is a generalization of DTM. So, the computability powers of NDTMs and DTM are equal, in sense of decidability. So, the Halting problem is not decidable by a NDTM. However, their time complexity is different.