The process of communication with consumers attracts the attention of companies. However, the issue of interpersonal communication has been under-researched. Consumers can adopt the brand as a result of communication with those who had adopted the brand (internal impact of the brand), or as a result of interactions with those who had adopted competing brands (the cross-brand effect). The paper shows that the interaction of internal and cross-brand impact can have a significant effect on the growth of the market. The focus is on the case of two identical competing brands with different time of entry into the market. Due to the internal impact of the brand, consumers can create an interaction-based advantage for the brand which first entered the market, and this advantage grows over time. Similarly, the cross-brand effect enables the accompanying brand to enjoy faster growth on the market.