Conditional constraints are frequently used to represent relations. To use these conditional constraints, it is necessary to develop an appropriate logic in which these conditional constraints can be represented and manipulated. Nevertheless, there has been little research that addresses interval-based conditional constraints. The proposed approach addresses the use of conditional constraints involving intervals in constraint networks. Two algorithms are presented: (1) a propagation algorithm for an interval-based conditional constraint, which is similar to one for an exact-value conditional constraint; (2) a propagation algorithm for interval-based conditional constraints which satisfy some conditions. The former can be applied to any conditional constraint. However, with the former algorithm, conditional constraints are usually categorized into the cases that they cannot be propagated. After investigating several methods in which most conditional constraints can be propagated, we propose the latter algorithm under certain condition that usually results in smaller resulting design space comparing to the former.