Glass transition behaviors of dilute aqueous solutions are currently unclear because the water crystallizes immediately below the fusion temperatures to prevent the determination. The behaviors of methanol aqueous solutions [(CH(3)OH)(x)(H(2)O)(1 - x)] were studied here by confining the solutions within silica-gel pores and following the enthalpy relaxation associated with the glass transitions by adiabatic calorimetry. The dilution of the solutions in the composition range x < 0.3 brought both abrupt increase in the glass transition temperature T(g) as referred to the composition dependence expected from the behavior in x > 0.3 and appearance of a new glass transition at around 115 K. It was conjectured from the results that a hydrogen-bond network inherent to water starts to develop at around x = 0.3, and that molecules on the pore wall cannot join the network by forming tetrahedrally extended hydrogen-bonds so that they should constitute a mobile layer as an interfacial one. Such a special layer is understood as absent above x > 0.3, indicating that no network structure inherent to water is developed in the solutions.