Annealing-induced changes in enthalpy relaxation and Curie temperature, T(c), were examined for amorphous (Fe0.85Ni0.15)90Zr10 and (Fe0.9Co0.1)90Zr10 alloys. The compositional dependence of an endothermic reaction was also examined for amorphous (Fe1-xCox)90Zr10 (x = 0-1) alloys. A reversible endothermic reaction occurs above the annealing temperature, T(a). The change in the magnitude of the endothermic peak, DELTAC(p,max), with T(a) shows a single stage with a peak at about T(x) - 400 K (i.e., the temperature that is 400 K lower than crystallization temperature). For (Fe1-xCox)90Zr10 alloys, the endothermic reaction is the largest at x = 0.5 and disappears at x = 0 and 1. The change in T(c) with T(a) is related to the increase in T(c) at T(a) congruent-to T(x) - 400 K, followed by the decrease in T, at temperatures above T(x) - 400 K. A good correspondence was observed between the reversible endothermic enthalpy relaxation and the increase in T(c) and between the irreversible exothermic enthalpy relaxation and the decrease in T(c). These results are explained as a consequence of the low-temperature endothermic reaction which is due to the local chemical ordering of Fe-Ni and Fe-Co atoms with shorter relaxation times. The exothermic reaction is mainly due to the long-range topological change leading to the densification of amorphous structure with longer relaxation times.