Abstract Smooth backfitting was first introduced in an additive regression setting via a direct projection alternative to the classic backfitting method by Buja, Hastie, and Tibshirani. This paper translates the original smooth backfitting concept to a survival model considering an additively structured hazard. The model allows for censoring and truncation patterns occurring in many applications, such as medical studies or actuarial reserving. Our estimators are shown to be a projection of the data into the space of multivariate hazard functions with smooth additive components. Hence, our hazard estimator is the closest nonparametric additive fit, even if the actual hazard rate is not additive. This is different from other additive structure estimators, where it is not clear what is being estimated if the model is not true. We provide full asymptotic theory for our estimators. We propose an implementation of estimators that shows good performance in practice.