Differential algebra based approaches are used to study a priori parameter identifiability of nonlinear systems with polynomial or rational functional forms. However, these methods cannot be applied to state-space models which have non-rational functions (e.g., exponential, sinusoidal etc.) of state variables. In this paper, we propose a method to test identifiability for systems with non-rational functions using Padé and power series approximations and differential algebra. In particular, for a certain class of systems, we show that if the approximation of a certain order is used and the resulting system is identifiable, then higher order approximations will also result in identifiable systems. The proposed approach is illustrated using a non-isothermal