Urotropin (U) and azelaic acid (AA) form 1:1 co-crystals (UA) that give rise to a rather complex diffraction pattern, the main features of which are diffuse rods and bands in addition to the Bragg reflections. UA is characterized by solvent inclusions, parasite phases, and high vacancy and dislocation densities. These defects compounded with the pronounced tendency of U to escape from the crystal edifice lead to at least seven exotic phase transitions (many of which barely manifest themselves in a differential scanning calorimetry trace). These involve different incommensurate phases and a peritectoid reaction in the recrystallization regime (T-h >0.6). The system may be understood as an OD (order-disorder) structure based on a layer with layer group P(c)c2 and cell a(o) similar or equal to 4.7, b similar or equal to 26.1 and c similar or equal to 14.4 Angstrom. At 338 K the layer stacking is random, but with decreasing temperature the build-up of an orthorhombic MDO (maximal degree of order) structure with cell a(1) = 2a(o), b(1) = b, c(1) = c and space group Pcc2 is begun (at similar to 301 K). The superposition structure of the OD system at T = 286 (1) K with space group Bmmb and cell (a) over cap = 2a(o), (b) over cap = b and (c) over cap = c/2 owes its cohesion to van der Waals interactions between the AA chains and to three types of hydrogen bonds of varied strength between U-U and U-AA. Before reaching completion, this MDO structure is transformed, at 282 K, into a monoclinic one with cell a(m) = a(o) + c/4, b(m) = b, c(m) = -2(a(o) + c/2), space group P2(1)/c, spontaneous deformation similar to2degrees, and ferroelastic domains. This transformation is achieved in two steps: first a furtive triggering transition, which is not yet fully understood, and second an improper ferroelastic transition. At similar to 233 K, the system reaches its ground state (cell a(M) = a(m), bM = b, c(M) = c(m) and space group P2(1)/c) via an irreversible transition. The phase transitions below 338 K are described by a model based on the interaction of two thermally activated slip systems. The OD structure is described in terms of a three-dimensional Monte Carlo model that involves first- and second-neighbour interactions along the a axis and first-neighbour interactions along the b and c axes. This model includes random shifts of the chains along their axes and satisfactorily accounts for most features that are seen in the observed diffraction pattern.