In this contribution, a novel approach for parametric modal analysis of second order systems with nonzero first order term is presented. This is particularly useful for modal analysis of locally linear systems. Based on a Taylor series representation of the system matrices, a numerical algorithm for obtaining a Taylor series expansion of the eingenmodes as well as the eigenvalues of the system is obtained. This is used to calculate a Taylor series representation of the matrices in the modal system representation which can subsequently be used for model order reduction. The method can handle multi-dimensional parameter spaces and systems with non-proportional damping.