It has been realised in the last few years that strong constraints on the time-variations of dimensionless fundamental constants of physics can be derived at any redshift from QSO absorption line systems. Variations of the fine structure constant, α, the proton-to-electron mass ratio, μ, or the combination, x=α2gp/μ, where gp is the proton gyromagnetic factor, have been constrained. However, for the latter two constants, the number of lines of sight where these measurements can be performed is limited. In particular the number of known molecular and 21 cm absorbers is small. Our group has started several surveys to search for these systems. Here is a summary of some of the characteristics of these absorbers that can be used to find these systems.