The transition probabilities of the lines 1¹S₀ - 2³P₀ and 1¹S₀ - 2³P₂ in He-like ions with nonzero nuclear spins are calculated. The hyperfine-quenching effect on the lifetimes of the 2³P_0,2 states is investigated. The Coulomb and Breit interelectronic interactions are taken into account to the order (αZ)²/Z by means of perturbation theory. The calculation is performed for both length and velocity gauges. The transition rates evaluated are in good agreement with previous 1/Z and CI calculations.