Studies of complex condensed matter systems have led to the discovery of materials of unexpected spatial organization as glasses, glassy crystals, quasicrystals, and protein and virus crystals. Here, we present two-dimensional (2D) short-range disordered molecular crystalline networks, which, regarding spatial organization, can be considered as surface analogues of 3D glassy crystals. In particular, the deposition of a flexible molecular module on Cu(111) gives rise to distinct phases whose characteristics have been examined in real space by scanning tunneling microscopy: a 2D short-range distortional disordered crystalline network and a 2D short-range orientational disordered crystalline network, respectively. Both phases exhibit a random arrangement of nanopores that are stabilized by the simultaneous presence of metal-organic and pyridyl-pyridyl interactions. The 2D short-range distortional disordered crystalline network displayed intriguing flexibility, as probed by the STM tip that modifies the pore shape, a prerequisite for adaptive behavior in host-guest processes.