Most marine species give rise to products of great economic importance in many countries. Fatty fish is attracting a great attention because of the beneficial role of fish lipids on human health. Many studies have shown that 0-3 fatty acids (the predominant polyunsaturated fatty acids [PUFA) in fish oil) have important roles in prevention of cardiovascular diseases and some types of cancer, including colon, breast and prostate. Oxidation of fat in fish causes detrimental effects on the quality of fish in terms of negative health effects and development of off flavor, color and textural changes. Water content and storage temperature are the major factors in controlling the lipid oxidation in fish. The aim of this research is to study the effect of moisture content and storage temperature during 80 days of storage on the fat oxidation of grouper which is an important fatty fish found in the Sultanate of Oman and negligible studies were conducted on the oxidation of fat during storage. Isopiestic method was used to determine the water activity (aw) of freeze-dried grouper samples. The BET and GAB equations were used for modeling the sorption isotherms of grouper samples. The Peroxide Value (PV) was used to evaluate the storage stability by indicating the level of primary oxidation of fat. Storage stability of grouper fish was conducted at two moisture levels (5 g/100 g sample and 20 g / 100 g sample) and five storage temperatures (-40, -20, 5, 25, and 40° C) respectively for 90 days . Thermal characteristics of freeze dried grouper equilibrated at different water activity were measured by Differential Scanning Calorimetry (DSC). The results showed that in both moisture levels no changes in PV-values was observed when samples were stored at -40°C (P>0.05) during 90 days of storage. In case of 5 g / 100 g moisture content stored at -20 and 5° C showed an exponential increase in PV-value and then level off to a nearly constant value, whereas at 25°C showed a peak. However sample stored 40° C did not show any peak instead an exponential decay of PV-values. In the case of 20 g / 100 g moisture content samples stored at -20° C showed an exponential increase. However, samples stored at 5° C showed an initial peak and then an exponential decline was observed, whereas samples stored at 25 and 40° C did not show any peak instead an exponential decay was observed. Water activity concept is commonly used in determining the stability of food. Foods are most stable close to their monolayer moisture value. The monolayer moisture for freeze-dried grouper was estimated as 6.2 g/100 g dry solids using BET-isotherm. The freeze-dried grouper stored at 5 g/ 100 g moisture content sample (5.3 g/100 g solids) was closed to its monolayer value, thus expected to be stable. However, it was found that samples only at -40° C, but higher temperature stored samples were found unstable even close to their monolayer moisture content. A shift in the base line of DSC thermo gram was observed; however it was difficult to confirm that it was the glass transition (T) since with increasing water content the sample did not plasticize (i.e. no decrease of the transition observed by baseline shift when water content was increased). In general it was very difficult to measure the Tg of freeze-dried grouper using DSC methods. Water activity and glass transition concepts did not valid in all experimental conditions.