Graphical Abstract: The paper explores the use of differential scanning calorimetry (DSC) and temperature modulated differential scanning calorimetry (TM DSC) to study α- and β- processes in amorphous sucrose and trehalose. The real part of the complex heat capacity is evaluated at the frequencies, f, from 5 to 20mHz. β-relaxations were studied by annealing glassy samples at different temperatures and subsequently heating at different rates in a differential scanning calorimeter.