I will analyze the strong CP problem in gauge models where QCD arises as a low-energy interaction emerging from the product of two non-abelian groups at around the TeV scale. A solution of the strong CP problem à la Peccei-Quinn in this class of models requires the introduction of two axions. The additional axion can be significantly heavier than the QCD one, making its phenomenology distinct from the one of the QCD axion.
