This thesis investigates techniques for modelling the steady state harmonic and interharmonic waveform distortion associated with HVDC links. Previous methods are reviewed and their associated problems discussed. A numerical frequency domain model of the single HVDC converter is presented. This is used to study the effects of applied waveform distortion, particularly on the commutation period, and leads to the development of a new linear small signal analytic model. The new model is extremely fast, accurate, and capable of directly predicting the returned harmonic and interharmonic spectra resulting from applied small signal waveform distortion. Frequency coupling matrices, calculated directly with the new model, are used to represent the time variant frequency modulating nature of the converter. These sparse matrices relate the linearised transfers of distortion through and around the converter and are used in a linear matrix equation that relates the inherent coupling between the ac side phase sequences and dc. Nodal analysis is then used to connect the full HVDC system together including rectifier, inverter and the ac and dc systems to form a sparse linear system admittance matrix. Solution speed is directly dependent on the matrix size and sparsity. This results in simple calculations used to pre-determine the main frequencies involved in the modulating process of the link. Both synchronous and asynchronous back-to-back link case studies are developed and the steady state harmonic and interharmonic waveform distortion validated against PSCAD/EMTDC time domain simulation. Finally, critical conditions for harmonic and interharmonic cross modulation are investigated. The effects of varying system impedance and operating point are examined, and worst-case scenarios demonstrated on a 50-50Hz back-to-back HVDC link with fundamental negative sequence unbalance on the rectifier terminals.