The two-dimensional (2D) polymeric spin crossover (SCO) compound Fe(py)2[Ag(CN)2]2 has been synthesized. The compound shows a two-step spin transition detected by magnetic, heat capacity, and X-ray diffraction measurements. The magnetic moment shows a high-temperature step (step 1) occurring at 146.3 K without hysteresis, while the low-temperature step (step 2) happens at 84 K on cooling and 98.2 K on heating. These measurements reveal a large amount of residual high spin (HS) species (23%) and that HS state trapping occurs at cooling rates of around 1 K min(-1) or higher. The two-step behavior has been confirmed by heat capacity, which gives, for steps 1 and 2, respectively, DeltaH1 = 3.33 kJ mol(-1), DeltaS1 = 22.6 J mol(-1) K(-1), and DeltaH2 = 1.51 kJ mol(-1), DeltaS2 = 15.7 J mol(-1) K(-1). For step 2 a hysteresis of 10 K has been determined with dynamic measurements. Powder X-ray diffraction at room temperature shows that the compound is isostructural to Cd(py)2[Ag(CN)2]2 previously reported. Powder X-ray diffraction indicates that there is only one crystallographic site for iron(II) in the whole temperature range, confirmed by Mössbauer spectroscopy. The X-ray diffraction study at different temperatures do not show any superstructure in the region between the transitions, discarding a crystallographic phase transition as the origin of the two-step behavior. However, an unexpected increase of the thermal factor is detected on lowering the temperature and considered as a manifestation of a disordered state between the two steps, consisting of a mixing of HS and LS species without long-range order.