The authors consider space-times with two spacelike commuting Killing fields. They evaluate the Riemann, the Ricci and the Einstein tensors in an orthonormal frame and by making a suitable choice of variables they reduce the vacuum Einstein equations to a simple complex Ernst equation. They show that one obtains complex Ernst equations for both, the norm and the twist of one of the Killing fields as well as for certain algebraic combinations of the norm and the inner product of the two Killing fields. They establish that in much the same way as the simplest solution of the former Ernst equation (for stationary axisymmetric space-times) leads to the Kerr black hole solution, the simplest solution of the latter Ernst equation describes the interaction region which results from the collision of two plane impulsive gravitational waves, previously obtained by Nutku and Halil. They further analyze this solution. They express it in null coordinates and they extend it to form a \(C^ 0\) space-time representing the different stages of the collision. They also describe it in a Newman-Penrose formalism and establish the development of a spacelike curvature singularity a finite time to the future of the collision. Considerations about the uniqueness of the resulting solution are also discussed.