The infrared absorption spectrum of solid CD4 has been studied in detail in the frequency range between 2000 and 7000 cm(-1). In the three normal-pressure phases of CD4 between 30 and 2 K, 25 weak overtone and combination bands have been observed. They have been tentatively assigned on the basis of their energies, structures, and intensities. Overtones of order upsilon(4) of the bending mode upsilon(4) have been detected for upsilon(4)=2, 3, 4, 6. As upsilon increases, one observes the transition from a regime where propagating vibrons are created on different molecules, to a regime where multivibron transitions occur on single molecules. Such behavior is triggered by changes in the intramolecular anharmonicity, which plays the role of a vibron-vibron binding energy.