Near-infrared luminescence is observed from single crystals of K2PdCl4 and K2PdBr4 between 13500 cm(-1) and 9000 cm(-1) (740 nm and 1100 nm). The emission spectrum of K2PdBr4 shows vibronic structure involving both the totally symmetrical a(1g) mode and the non-totally symmetrical b(1g) mode (D-4h point group). The luminescence spectrum of K2PdCl4 is less resolved, but shows similar vibronic structure. The maxima of the weak lowest energy absorption bands are at 14800 cm(-1) (molar absorptivity=0.42 M(-1) cm(-1)) and 14645 cm(-1) (molar absorptivity=0.38 M(-1) cm(-1)) at 8 K for K2PdCl4 and K2PdBr4, respectively. The Stokes shifts for K2PdCl4 and K2PdBr4 are 3865 and 3420 cm(-1). A gap of approximately 700 (K2PdCl4) or 950 cm(-1) (K2PdBr4) separates the emission and absorption spectra. This energy gap and the vibronic structure are analyzed with a model involving the E(g)xb(1g) Jahn-Teller effect in the (3)E(g) excited state of the square-planar [PdCl4](2-) and [PdBr4](2-) complexes. The Huang-Rhys parameters S-a1g and S-b1g are 6.7 and 0.2 for K2PdCl4, leading to bond elongations of 0.12 Angstrom for each of two opposing Pd-Cl bonds and of 0.09 Angstrom for each of the other two bonds. The corresponding values for K2PdBr4 are 7.6 (S-a1g), 0.4 (S-b1g), 0.12 Angstrom and 0.07 Angstrom.