An intuitive picture of Lambda-doubling in diatomic molecules is presented using a semiclassical theory. A common view of Lambda-doubling as arising from electrons ''lagging'' behind the rotating internuclear axis is shown to be misleading; rather, the eigenfunctions are symmetric about the molecular axes and can be expressed as a superposition of pure nonrotating orbitals and travelling waves. These results are shown to be consistent with a full quantum treatment. We also examine, for the first time, time-dependent states, by monitoring expectation values of electronic- and nuclear-angular momenta. For low rotation frequency, the expectation value of the electronic-angular momentum locks onto the rotating internuclear axis, while for high rotation frequency it locks onto the space-fixed total-angular momentum axis. At intermediate frequencies is a complicated behavior. (C) 1997 American Institute of Physics.