We investigate the optical conductivity of photogenerated solitons in quasi-one-dimensional halogen-bridged binuclear transition-metal (MMX) complexes with particular emphasis on a comparison among the three distinct groups: A 4 [Pt 2 (P 2 O 5 H 2 ) 4 X]$nH 2 O (XZCl, Br, I; AZ Na, K, NH 4 ,.), Pt 2 (RCS 2 ) 4 I (RZC n H 2nC1 ,) and Ni 2 (CH 3 CS 2 ) 4 I which exhibit a mixed-valent ground state with the X sublattice dimerized, that with the M 2 sublattice dimerized and a Mott-Hubbard magnetic ground state, respectively. Soliton-induced absorption spectra for A 4 [Pt 2 (P 2 O 5 H 2 ) 4 X]$nH 2 O should split into two bands, while that for Pt 2 (RCS 2 ) 4 I and Ni 2 (CH 3 CS 2 ) 4 I should consist of a single band. The excitonic effect is significant in Ni 2 (CH 3 CS 2 ) 4 I. q MX chains, that is, a family of quasi-one-dimensional halogen (X)-bridged transition-metal (M) complexes, provide an exciting stage [1-4] performed by electronelectron correlation, electron-lattice interaction, low dimensionality and d-p orbital hybridization. In recent years, binuclear metal analogs which are referred to as MMX chains have stimulated renewed interest [5,6] in this system. The existent MMX compounds consist of three groups: A 4 [Pt 2 (pop) 4 X]$nH 2 O (XZCl, Br, I; AZLi, Cs,.; popZ diphosphonateZP 2 O 5 H 2K 2 ) [7,8], Pt 2 (RCS 2 ) 4 I (RZalkyl chainZC n H 2nCl ) [9,10] and Ni 2 (dta) 4 I (dtaZdithioacetate ZCH 3 CS K 2 ) [11]. A 4 [Pt 2 (pop) 4 X]$nH 2 O resembles conventional MX compounds and generally exhibits a similar ground state of mixed valence with halogen-sublattice dimerization [12,13], which is referred to as the chargedensity-wave (CDW) state. Pt 2 (RCS 2 ) 4 I exhibits a distinct ground state with metal-sublattice dimerization [14], which is referred to as the alternate charge-polarization (ACP) state. Ni 2 (dta) 4 I exhibits the averaged-valence state without any lattice distortion [15] and is regarded as an insulator of the Mott-Hubbard (MH) type. These ground states can be tuned by pressure [16][17][18][19] as well as replacing the bridging halogens [13,20], counter ions [18,21] and ligand molecules [22].In such circumstances, topological excitations [23] such as solitons and polarons have been found for an MMX Hamiltonian of the Su-Schrieffer-Heeger type [24] and an analogy between MMX chains and trans-polyacetylene has been pointed out. The direct Mðd z 2 ÞK Mðd z 2 Þ overlap effectively reduces the on-site Coulomb repulsion and therefore electrons can be more itinerant in MMX chains. In fact MMX chains exhibit much higher room-temperature conductivity than MX chains [14]. Solitons generally have lower formation energies and smaller effective masses than polarons in MMX chains [25]. Then we take more and more interest in MMX solitons as charge or spin carriers. While MMX uniform absorption spectra have recently been investigated [26], but photoinduced ones, which serve as prominent probes for nonlinear excitations, have neither measured nor calculated yet. Thus motivated, we study optical conductivity fo...