The introduction of the GSSP concept has been successful to the extent that it has fostered a considerable amount of stratigraphic studies. It has also led to a re-thinking of stratigraphic principles and practices. Chronostratigraphy as practiced today attempts to reconcile two opposite philosophical principles, the rock-time model of Hedberg and the time-rock model of Harland. I argue here that the time-rock model does not serve chronostratigraphy well and that a return to Hedbergian principles is necessary to ensure the correct application of chronostratigraphic principles. As the definition of GSSPs for the Phanerozoic record is nearing completion, new complementary steps should be undertaken to strengthen the GSSP concept. One concerns the elaboration of frameworks of correlation so that GSSP sections would not stand isolated. The designation of reference sections at high latitude or in terrestrial records would validate this effort. Another concerns the re-introduction of unit stratotypes, for the benefit of the Astronomical Time Scale, and to broaden the use of chronohorizons for worldwide correlations. Both undertakings will foster continued scientific discussion and openness in the stratigraphic community.