Transonic flow with a local supersonic region (LSR) is studied numerically and analytically. The arising of shock waves is analyzed for small as well as large deviations of the airfoil shape from a shockless configuration. As shown, the coalescing of compression waves and formation of weak shocks are caused by either too small curvature of an airfoil portion, or the steepening of flow gradients due to accumulative phenomena in the LSR, or strong deceleration of the flow that occurs near the sonic line forestalling the development of the accumulative phenomena. In particular, wavy sonic line configurations obtained at off-design freestream Mach numbers in [9],[11] are accounted for by the interaction of the arising shocks with the sonic line.