[en] By imposing special compatible similarity constraints on a class of integrable partial q-difference equations of KdV-type we derive a hierarchy of second-degree ordinary q-difference equations. The lowest (non-trivial) member of this hierarchy is a second-order second-degree equation which can be considered as an analogue of equations in the class studied by Chazy. This second-order second-degree equation follows from a system in terms of two variables from which also follows an associated third-order first-degree equation. We present the isomonodromic deformation problem for the two-variable system and discuss the relation between the hierarchy of second-degree ordinary q-difference equations and other equations of Painleve type. (fast track communication)