The study of relational events, which are interactions occurring between actors over time, has gained significant traction recently. Traditional relational event models typically focus on modelling the occurrence and sequence of events without considering their duration even though duration information is frequently available in empirical relational event data. We introduce a novel Duration Relational Event Model (DuREM) that incorporates the temporal duration of events into the analysis. The proposed model extends the existing framework by (i) allowing the inclusion of past event durations in the endogenous statistics to account for how the duration of past events affects the rate of future interactions, and (ii) extending the traditional relational event model by also modelling when events will end based on past event history and covariates. This is achieved by extending the risk set to include both ongoing events at risk of ending and idle dyads at risk of starting new events. The methodology is implemented in a new R package `durem'. Two case studies concerning team dynamics and inter-personal violence are presented to illustrate the applicability of the model.