A new type of mode conversion between two linear waves in a nonuniform medium is investigated. Single-crossing conversion occurs when a ray of one wave crossestransverselythe dispersion manifold of another wave.Double-crossingmode conversion theory describes when the ray punctures the dispersion manifold twice due to raycurvature. To study this new process, a one dimensionally nonuniform background medium is considered, which gives rise to four scenarios. These scenarios are distinguished on the basis of whether the two waves have equal or opposite energy signs, and whether they are copropagating or counterpropagating. Usingmodular-eikonal theory (suitable for multiple crossings), each scenario is first studied analytically by constructing anS-matrix relation between theoutgoingandincomingasymptotic wave amplitudes. The analytical results are then compared with numerical results and excellent agreement is found. ©1998 American Institute of Physics.