The effect of pressure on the thermal dependence of the magnetic susceptibility has been investigated in the 2,2 ' -bipyrimidine (bpm)-bridged iron(II) complexes of formula {[Fe(L)(NCX)(2)](2)bpm} (X = S and Se; L = bpm and bt (2,2 ' -bithiazoline)) and [Fe(bpm)(NCX)(2)](n). At ambient pressure, the compound {[Fe(bpm)(NCS)(2)](2)bpm} (A) is paramagnetic in the temperature region 4-300 K and shows the intramolecular antiferromagnetic interaction. At P = 8.9 kbar, A undergoes spin transition, T-c approximate to 150 K, involving 50% of iron atoms and ultimately causing the disappearance of antiferromagnetic coupling. At intermediate pressures the interplay between the intramolecular interaction and spin transition was studied, At 1 bar, {[Fe(bpm)(NCSe)(2)](2)bpm} (B) undergoes a 50% spin transition, T-c approximate to 120 K, similar to that of A at 9.8 kbar. As pressure was increased, B showed the occurrence of a two-step spin transition which is complete at P = 10.3 kbar at low temperatures. Our study gives the evidence of formation of HS-LS species from HS-HS pairs in dinuclear compounds during the thermal or pressure-induced spin crossover, which is reflected in the buildup of a plateau in the middle part of the two-step continuous curve. Magnetization versus magnetic field curves of A and B at I bar at 1.9 K give support for the occurrence of almost 100% of mixed spin pair LS-HS state species in the low-temperature plateau corresponding to the 50% spin transition for B. The compounds [Fe(bpm)(NCS)(2)](n), and {[Fe(bt)(NCSe)(2)](2)bpm} have similar thermal dependences of the magnetic properties under pressure as those of A and B. respectively. In the particular case of dinuclear compounds, it is shown that application of external hydrostatic pressure discloses common features of the whole class of these compounds, which usually can only be revealed by variation of chemical composition.