A method for the precision machining of flanks of gear-wheel-shaped workpieces, in particular those with convex teeth, using an internally toothed tool with crossed axes, in which simultaneous relative movements take place not only in three mutually perpendicular axes but also around an axis perpendicular to the cross-axes angle such that not only the tooth flanks of the tool and the workpiece have tangential contact with one another but also the base body of the tool and of the workpiece touch one another at a point of contact IV of which the position changes continuously, and a straight line g orthogonally penetrating the base body of the tool and the base body of the workpiece at the point of contact not only intersects the axis C1 of the workpiece or of its base body and the axis C2 of the tool or its base body (points III, II), but also passes through the center I of an ideal sphere K1 which adapts itself to the base body of the workpiece at the point of contact IV. If a tool with convex teeth is used, the straight line g should also pass through the center V of an ideal sphere K2 which adapts to the base body of the tool at the point of contact IV. In addition, tools suitable for this method are proposed and possible ways of appropriately dressing them.