The electronic structures of Y Ba2Cu3Ox and YBa2Cu4O8 were studied by angleresolved photoemission with an energy resolution of better than 10 meV. A detailed study in the 1st and 2nd Brillouin zone of untwinned single crystals shows the presence of “extended” saddle point singularities in the band structure in the vicinity of the Fermi energy, which give rise to van Hove singularities in the density of states. The binding energy of the singularity depends on the doping. We show that this extended saddle point singularity leads to a density of states which diverges as e−1/2, which in turn can lead to very high transition temperatures even in a BCS scheme with weak coupling.