This article studies the stability crossing set of linear time-invariant systems with two scalar-delay channels. This study is crucial to the complete stability analysis along the idea of D-subdivision method. The characteristic quasipolynomial of such systems contains an exponential term with the sum of two delays in its exponent (cross term). A complete parameterization and geometric characterization of the stability crossing set is conducted. It was found instrumental to relate it to an associated quasipolynomial without such a cross term through an elimination process. However, a spurious stability crossing set may arise in this process. A revised parameterization method is derived that automatically eliminates such a spurious stability crossing set. (C) 2013 Elsevier Ltd. All rights reserved.