Evolutionary structures were observed in as-melt spun ribbons of Al-3.5Mn-0.8Co, Al-3.5Mn-1.3Co, Al-3.5Mn-2Co, Al-5Mn-0.8Co and Al-5Mn-2Co alloys. The evolutionary structures contained two zones, zone A and zone B, at the chilled and unchilled sides, respectively. A banded structure was observed between the two zones as a transitional region in the Al-3.5Mn-1.3Co alloy. The enthalpy differences, DELTAH(O)ne, between a non-equilibrium state in as-melt spun ribbons and the equilibrium state in fully annealed ribbons of the Al-Mn-Co alloys were evaluated using data obtained by differential scanning calorimetry (DSC) measurements. The values of DELTAH(O)ne for Al-Mn-Co alloys are lower than those for Al-Mn binary alloys. DELTAH(O)ne corresponds to a decrease in Gibbs free energy, DELTAG, which is stored in a solidified solid during rapid solidification. The formation of the banded structure is interpreted on the basis of an analysis of the distribution of DELTAH(O)ne or the fluctuation in DELTAG, which should oscillate in order to correspond with a gradual reduction of cooling ability for the constrained solidification by the substrate.