A characteristic of existing predictive process monitoring techniques is to first construct a predictive model based on past process executions, and then use it to predict the future of new ongoing cases, without the possibility of updating it with new cases when they complete their execution. This can make predictive process monitoring too rigid to deal with the variability of processes working in real environments that continuously evolve and/or exhibit new variant behaviors over time. As a solution to this problem, we propose the use of algorithms that allow the incremental construction of the predictive model. These incremental learning algorithms update the model whenever new cases become available so that the predictive model evolves over time to fit the current circumstances. The algorithms have been implemented using different case encoding strategies and evaluated on a number of real and synthetic datasets. The results provide a first evidence of the potential of incremental learning strategies for predicting process monitoring in real environments, and of the impact of different case encoding strategies in this setting.