One of the top ecological priorities is to find sensitive indicators for pollution monitoring. This study focuses on the bioconcentration and responses (condition index, survival, oxygen consumption, heart rates, and oxidative stress and neurotoxic effect biomarkers) of mussels from the Volga River basin, Dreissena polymorpha and Dreissena bugensis, to long-term exposure to toxic chemicals such as tributyltin (TBT, 25 and 100 ng/L) and copper (Cu, 100 and 1000 μg/L). We found that TBT was present in the tissues of zebra and quagga mussels in comparable amounts, whereas the bioconcentration factor of Cu varied depending on its concentration in water. Differences in responses between the two species were revealed. When exposed to high Cu concentrations or a Cu-TBT mixture, quagga mussels had a lower survival rate and a longer heart rate recovery time than zebra mussels. TBT treatment caused neurotoxicity (decreased acetylcholinesterase activity) and oxidative stress (increased levels of thiobarbituric acid reactive substances) in both species. TBT and Cu levels in mussel tissues correlated positively with the condition index, but correlated with the level of acetylcholinesterase in the mussel gills. The principal component analysis revealed three main components: the first consists of linear combinations of 14 variables reflecting TBT water pollution, TBT and Cu levels in mussel tissues, and biochemical indicators; the second includes Cu water concentration, cardiac tolerance, and mussel size; and the third combines weight, metabolic rate, and heart rates. Quagga mussels are less tolerable to contaminants than zebra mussels, so they may be used as a sensitive indicator.