Proactive User Interfaces (PUIs) aim at facilitating the interaction with a user interface, e.g., by highlighting fields or adapting the interface. For that purpose, they need to be able to predict the next user action from the interaction history. In this paper, we give an overview of sequence prediction algorithms (SPAs) that are applied in this domain, and build upon them to develop two new algorithms that base on combining different order Markov models. We identify the special requirements that PUIs pose on these algorithms, and evaluate the performance of the SPAs in this regard. For that purpose, we use three datasets with real usage-data and synthesize further data with specific characteristics. Our relatively simple yet efficient algorithm FxL performs extremely well in the domain of SPAs which make it a prime candidate for integration in a PUI. To facilitate further research in this field, we provide a Perl library that contains all presented algorithms and tools for the ...