The evolution of the leakage current in high-K lanthanum oxide films in MOS devices caused by the application of progressive electrical stress is investigated. The degradation method consists in performing successive voltage sweeps using an ever increasing voltage range with the aim of generating incremental damage to the structure in a controlled manner. We show that the total current flowing through the device can be thought of as formed by two parallel components, one associated with the tunneling mechanism and the other one associated with diode-like conduction. This latter component evolves with applied stress. It is shown the importance of considering series and parallel resistances in order to account for the right shape of the conduction characteristics. Analytical expressions for both current contributions suitable for all stages of degradation and bias conditions are provided.