Storyline visualizations are a popular way of visualizing characters and their interactions over time: Characters are drawn as x-monotone curves and interactions are visualized through close proximity of the corresponding character curves in a vertical strip. Existing methods to generate storylines assume a total ordering of the interactions, although real-world data often do not contain such a total order. Instead, multiple interactions are often grouped into coarser time intervals such as years. We exploit this grouping property by introducing a new model called storylines with time intervals and present two methods to minimize the number of crossings and horizontal space usage. We then evaluate these algorithms on a small benchmark set to show their effectiveness. * Alexander Dobler was supported by the Vienna Science and Technology Fund (WWTF)[10.47379/ICT19035]. Anaïs Villedieu was supported by the Austrian Science Fund (FWF) under grant P31119. We thank Martin Gronemann for the initial discussion.