Aspects of the geological monitoring of the volcanic island of Surtsey 1967-1998, are described. A hydrothermal system was developed within the tephra craters in late 1966 to early 1967. Temperatures in a drill hole, situated at the eastern border of the hydrothermal area, indicate that the hydrothermal system at that site has been cooling at an average rate of ≤ 1°C per year since 1980. The tephra was altered rapidly within the hydrothermal area, producing the first visible palagonite tuff in 1969. A substantial part of the tephra pile above sea level was probably converted to tuff by 1972. The visible area of tuff has gradually increased since then, primarily due to erosion of tephra at the surface. By 1998 52% of the exposed tephra area had been converted to palagonite tuff. By volume, however, some 80-85% of the tephra pile above sea level has been converted to tuff in 1998. The area of Surtsey has shrunk from its original 2.65 km² (1967) to 1.47 km² (1998) due to marine abrasion. The geological formations on Surtsey have, however, responded quite variably to erosion. The tephra pile was easily eroded, but marine abrasion. The central core of palagonite tuff is estimated to be ≤0.39 km². Statistical estimation of models of the decreases of Surtsey indicate that it will last for a long time. The numerical experiments indicate that it will take over 100 years until only the palagonite tuff core is left. It is postulated that the final remnany of Surtsey before complete destruction will be a palagonite tuff crag, comparable to those of the other islands in the Vestmannaeyjar archipelago.