In many practical situations, uncertainty with which we know each quantity is described by an interval. In processing such data, it is useful to know that the sum of two intervals is always an interval. In some cases, however, the set of all possible value of a quantity is described by a bi-interval -- i.e., by a union of two intervals. It is known that the sum of two bi-intervals is not always a bi-interval. In this paper, we describe all the class of bi-intervals which are closed under addition -- i.e., for which the sum of bi-intervals is a bi-interval.