Combustion systems with swirl chambers are applied in some spark ignition engines with homogeneous mixture. Such systems are developed to burn lean mixture with increased compression ratio far from the knock limit [1,2]. It was shown that these systems could be significantly improved by employing a prechamber with a catalyst [3,4]. An important part of the discussed combustion systems is cylindrical combustion chamber with a strong swirl. In this chamber, the flame propagates in the field of centrifugal forces increasing with a radius. In such conditions the flame surface takes the form of a cylinder. In the past, in a few experimental studies the behavior of flame propagation was investigated under the action of increased centrifugal forces, but the results were qualitative in nature [5, 6 and 7]. In the proposed paper an experimental study of flame propagating in a mixture with rigid-body rotation was carried out. The experiments were performed in a closed cylindrical vessel with transparent walls. The effect of the rotation rate on flame behavior, flammability limits, propagation velocity, flame extinction at the wall and some other parameters were investigated. The flame propagating in a swirling mixture is axisymmetric. At the beginning it propagates from the ignition point in axial direction. After touching the side-wall of the cylindrical vessel the flame starts to propagate in radial direction. In some conditions, when the mixture composition is lean or the rotation rate is high, the flame can be locally quenched at the contact surface with the walls. The axial propagation velocity of the flame increases and the radial propagation velocity decreases, with the rise of the rotation rate. Conclusions related to the combustion systems with swirl chambers applied to spark ignition engines are summarized at the end of the paper.