For adults and children, genetic and environmental factors are known to affect brain structure and neural activity necessary for conducting various cognitive tasks. However, little is known regarding genetic and environmental contributions to individual differences in neural activity during the first two years of life. Concentrations of oxygenated and deoxygenated hemoglobin were measured bilaterally over temporal areas of 7 monozygotic and 17 dizygotic twin pairs using near-infrared spectroscopy. Results showed that environmental influences on the concentration of hemoglobin were larger than for genetic influences. Significant genetic and environmental influences were detected in different temporal areas. We discuss the genetic and environmental influences on the hemodynamic response to speech stimuli during the first two years of life.