Basing on materials of research expeditions and fishing cruises to the Kerguelen Islands shelf in the period from 1970 to 1991, dynamics of size- age structure of marbled rockcod (Notothenia rossii rossii) population is shown. Data on age determination for 1970-1989 (Tankevich, 1990) and the data collected in the joint Soviet-French expedition on board RTMA Orlinoye in May-Jine 1991 were used to characterise the age composition. It was determined that in the initial years of exploitation of the stock, the major part of catches (more than 80%) was formed by repeated spawning fish. then as a result of fisheries, the share of the fish spawning for the first time increased considerably in catches and in some years (1981-1985) fisheries were based practically on recruitment. After the closure of the specialised fishery in 1985 and after the marbled rockcod by-catch at other fisheries was limited to 500 tons, a stable trend towards increase in the mean age and fish length was noted in catches. In May-June 1991 the mean length was 59.2 cm, mean age was 7.4 years; some 70% of catch consisted of repeated spawning fish. The author consideers the demographic populational structure in 1991 to be close to that observed in the initial years of exploitation and further closure of marbled rockcod specialised fishery can lead to increase in natural mortality of the population as the whole. Fish removal of older age groups is recommended to start in the nearest years. It will make it possible to control size- age structure changes in the spawning part of the population.