Physiological capabilities and fermentation performance of Saccharomyces cerevisiae strains to be employed during industrial wine fermentations are critical for the quality of the final product. During the process of biomass propagation, yeast cells are dynamically exposed to a mixed and interrelated group of known stresses such as osmotic, oxidative, thermic, and/or starvation. These stressing conditions can dramatically affect the parameters of the fermentation process and the technological abilities of the yeast, e.g., the biomass yield and its fermentative capacity. Although a good knowledge exists of the behavior of S. cerevisiae under laboratory conditions, insufficient knowledge is available about yeast stress responses under the specific media and growth conditions during industrial processes. We performed growth experiments using bench-top fermentors and employed a molecular marker approach (changes in expression levels of five stress-related genes) to investigate how the cells respond to environmental changes during the process of yeast biomass production. The data show that in addition to the general stress response pathway, using the HSP12 gene as a marker, other specific stress response pathways were induced, as indicated by the changes detected in the mRNA levels of two stress-related genes, GPD1 and TRX2. These results suggest that the cells were affected by osmotic and oxidative stresses, demonstrating that these are the major causes of the stress response throughout the process of wine yeast biomass production.