Summary: We study the homological finiteness property \(F P_n\) of fibre products. A homological version of the \(n -(n + 1) -(n + 2)\) Conjecture is suggested and solved in some cases. Though the Homological 1-2-3 Conjecture is still open, we prove a homological version of the Virtual Surjection Conjecture in the case of virtual surjection on pairs.