The return of its stock exchange and the companies traded within are one of the important indicators for a national economy. Due to the global structure of stock markets, returns are closely related to both national and international market variables. This study makes a comparative analysis of the volatility structures of the energy companies traded in the Kazakhstan Stock Exchange (KASE) and the combined stock market index and gold and oil prices in international markets for the period between January 01, 2021, and June 31, 2023. The research focused on two issues. The first is the analysis of the volatility structure of the six series examined. For this purpose, four different models were examined. The second focus is to determine whether the returns in international indices have a causal effect on the Kazakhstan stock market (composite stock market index) and the returns of oil and energy companies traded in the stock market. The results revealed that other indices and returns have a similar variable variance structure, except for the KASE. The relevant coefficient estimation was found to be significant in both conditional standard deviation models for the KASE index. The coefficient estimate of the GARCH-M(1,1) model in the OIL index was significant, whereas conditional standard deviation models and the relevant coefficients of both conditional standard deviation models were found to be statistically insignificant in the other returns. This is an indication of the structural compatibility of Kazakhstan's stock market composite index and energy and oil companies with international markets. Furthermore, the causality analysis results showing that international indices have a causal effect on KASE and KZAP is another indicator that the Kazakhstan market works in harmony with the international markets.