A lamellar ABA triblock copolymer brought to equilibrium in the presence of a B-compatible solvent generally swells or transforms into an A-dispersed (cylindrical or micellar) morphology, depending on solvent content. If the A blocks of the copolymer are glassy, they serve as physical cross-links and stabilize a gel network in which A microdomains are linked through a combination of connected B bridges and entangled B loops. An alternate route by which to introduce solvent into a triblock copolymer, as well as retain the local molecular anisotropy (and bridge population) of the initial lamellar morphology, is to selectively swell the B block and, at sufficiently high solvent concentrations, produce a mesogel. In this work, we describe the formation of mesogels from two chemically related triblock copolymers and employ dynamic mechanical analysis and transmission electron microscopy to examine the features of the resultant nonequilibrium materials.