An electromagnetic-brake cooling structure of a phase-variable device having an electromagnetic brake means (40) and varying the phase of a camshaft, wherein engine oil in an oil sump (74) on the radial inner side of a clutch case (60) led to the relative sliding surfaces of a friction material (66) and a rotary drum (44) through a notch (61) provided in the clutch case (60) at the front edge part of the inner peripheral wall of the clutch case (60), a notch (61b) for leading oil to the front edge part of the clutch case outer peripheral wall (60b), the oil on the relative sliding surfaces of the friction material (66) and the rotary drum (44) is discharged positively to the outside, and the circulation of the cooling oil is activated to increase the cooling effect of the sliding surface of the friction material (66).