Deformation and relaxation properties of hypercrosslinked polystyrene networks have been studied by thermomechanical method at a uniaxial compression using individual spherical beads of the polymer. The networks examined were prepared by postcrosslinking of highly swollen beads of a styrene-0.3% DVB copolymer with 0.3-0.75 mole of monochlorodimethyl ether, which results in the introduction of 0.6-1.5 methylene bridges between each two polystyrene phenyl rings. The polymers obtained are shown to belong neither to typical glassy materials, nor to typical elastomers. Though no characteristic plateau of rubberlike elasticity was observed on the deformation curves of the beads, the polymers exhibit two fundamentally important features of the rubberlike state: The deformations are large (up to 30-40% of the initial diameter) and reversible. Relaxation of residual deformations, however, requires prolonged heating of the sample, or a cycle of swelling and drying. The deformation can start in the temperature range from -70 to +150 degrees C depending on pressure applied. The crosslinking degree in the range from 40-100% and higher does not affect noticeably the behavior of the hypercrosslinked polystyrene. Nature of the high mobility of the hyper-crosslinked network is discussed.