In the series of polymeric spin-crossover compounds Fe(X-py)(2)[Ag(CN)(2))](2) (py=pyridine, X=H, 3-Cl, 3-methyl, 4-methyl, 3,4-dimethyl), magnetic and calorimetric measurements have revealed that the conversion from the high-spin (HS) to the low-spin (LS) state occurs by two-step transitions for three out of five members of the family (X=H, 4-methyl, and X=3,4-dimethyl). The two other compounds (X=3-Cl and 3-methyl) show respectively an incomplete spin transition and no transition at all, the latter remaining in the HS state in the whole temperature range. The spin-crossover behaviour of the compound undergoing two-step transitions is well described by a thermodynamic model that considers both steps. Calculations with this model show low cooperativity in this type of systems. Reflectivity and photomagnetic experiments reveal that all of the compounds except that with X=3-methyl undergo light-induced excited spin state trapping (LIESST) at low temperatures. Isothermal HS-to-LS relaxation curves at different temperatures support the low-cooperativity character by following an exponential decay law, although in the thermally activated regime and for aX=H and X=3,4-dimethyl the behaviour is well described by a double exponential function in accordance with the two-step thermal spin transition. The thermodynamic parameters determined from this isothermal analysis were used for simulation of thermal relaxation curves, which nicely reproduce the experimental data.< Réduire