The extreme Schwarzschild-de Sitter space-timeis a spherically symmetric solution of Einstein'sequations with a cosmological constant Lambda and massparameter m > 0 which is characterized by thecondition that 9Λm2 = 1. The globalstructure of this space-time is here analyzed in detail.Conformal and embedding diagrams are constructed, andsynchronous coordinates which are suitable for a discussion of the cosmic no-hair conjecture arepresented. The permitted geodesic motions are alsoanalyzed. By a careful investigation of the geodesicsand the equations of geodesic deviation, it is shown that specific families of observers escape fromfalling into the singularity and approach nonsingularasymptotic regions which are represented by special“points” in the complete conformal diagram.The redshift of signals emitted by particles whichfall into the singularity, as detected by those observers which escape, is also calculated.