A possibility of formation of bound states (BSs) of two solitons belonging to two channels carried by different wavelengths in a dispersion-managed (DM) system is considered. An estimate demonstrates that this is possible if the wavelength separation between the channels is ∼0.1 nm, the temporal width of the solitons is ∼10 ps, and their peak power is ∼1 W. We study the BSs by dint of both the variational approximation (VA), based on the Gaussian ansatz, and direct numerical simulations. In all the cases, predictions of VA compare very well with numerical results. A symmetric system, with equal path-average dispersion (PAD) in both channels (which may be zero, anomalous, or normal), is considered, as well as cases of zero PAD in one channel and either anomalous or normal PAD in the other one, and opposite signs of PAD in the two channels. In all the cases, it is found that stable BSs exist indeed, provided that their energy exceeds a certain minimum, which depends on the values of PAD in the channels and the inverse-group-velocity difference between them. There is a critical value of the latter parameter, such that no BS is possible if the inverse-group-velocity difference exceeds the critical value. It is also demonstrated that, in the case when PAD in one channel is normal and large, so that a DM soliton is unstable in it, the interaction with a soliton in a channel with anomalous PAD can produce a completely stable BS.