In this paper the issue of local structural identifiability of high-order state space models with non-linear parametrizations is addressed. Two methods are presented that provide analytical expressions for information matrices of which the rank determines identifiability. The first method requires solving a Lyapunov equation of high dimension and is applicable only to stable models. The second method applies also to unstable models and is based on a gradient computation algorithm by dynamic programming, that normally is used in an identification framework.