It has often been claimed that random non-equilibrium mechanisms can result in apparent homotropic and heterotropic effects in steady-state kinetics of the kind more usually attributed to intersubunit allosteric interactions. However, it has never been shown whether any simple random mechanism could in fact give patterns of apparent interaction similar to those predicted by the well-known allosteric models. The patterns of apparent substrate co-operativity and affinity given by the steady-state of a standard simple random substrate-modifier mechanism in which catalytic velocity is proportional to substrate binding have been analysed mathematically and numerically. All patterns possible with this model are described. Some of them rather resemble those possible with standard allosteric models, in that there is a high-affinity and a low-affinity form at zero and infinite modifier concentrations (or vice versa) which show Michaelian behaviour, apparent co-operativity passing through a maximum or minimum at intermediate affinities. Unlike the allosteric models the family of curves is in principle not symmetrical. The random model can also give behaviour not possible with the standard allosteric models, such as higher substrate affinity at intermediate modifier concentrations than at either zero or infinite modifier, with concomitant negative apparent substrate co-operativity, or a single change of sign of apparent substrate co-operativity. The analysis uses recently discovered simplified forms of steady-state equations for random models.