We consider general even ferromagnetic systems with pair interactions in a nonnegative external magnetic fieldh. Classes of single-site measures are found such that the GHS inequality is valid for allh h, whereh 0 is a number depending on but independent of the size of the system. These measures include both absolutely continuous and discrete measures. For =a 0+{(1–a)/2} · ( 1 + –1), somea [0, 1),h is determined exactly.