We investigate the thermodynamical properties of an adapted ANNNI-like (axial next nearest neighbour Ising-like) model for 1D spin crossover solids. We performed an exact treatment within the framework of the well known transfer matrix method and derived the thermal evolution of the high spin fraction, the correlation function and the heat capacity. We show that a model of competition of the interactions between similar spin state ions reproduces qualitatively the main features of experimental data: gradual, abrupt and two-step spin crossover transitions. In addition, we found that the intermediate region of the two-step transition exhibits two types of spatial organization, according to the sign of the interactions. Indeed, antiferro-like and 'antiphase' (called the phase in the ANNNI model) structures are obtained. We also found that these two configurations can be distinguished through the thermal evolution of their corresponding correlation functions. The existence of the phase , predicted by the present model, is in good agreement with recent observations on a spin crossover sample of [{Fe(CNBH3)(4phpy)}2(μ-bpypz) 2] for which this phase was evidenced for the first time, in these materials. © 2007 IOP Publishing Ltd.