It is a fundamental problem of identification to be able-even before the data have been analyzed-to decide if all the free parameters of a model structure can be uniquely recovered from data. This is the issue of global identifiability. In this contribution we show how global identifiability for an arbitrary model structure (basically with analytic non-linearities) can be analyzed using concepts and algorithms from differential algebra. It is shown how the question of global structural identifiability is reduced to the question of whether the given model structure can be rearranged as a linear regression. An explicit algorithm to test this is also given. Furthermore, the question of ’persistent excitation’ for the input can also be tested explicitly is a similar fashion. The algorithms involved are very well suited for implementation in computer algebra. One such implementation is also described.