New Delhi, Dec. 4 -- Global fashion and personal-care brands are scrambling to enter India, attracted by rising affluence and evolving consumer aspirations in the world's fastest-growing major economy, even as demand cools in other key markets.

Large international clothing labels such as COS, Bershka, Next, and G-Star Raw, and cosmetics brand Lush have entered the Indian market over the past year. Canadian athleisure Lululemon and American contemporary clothing retailer Abercrombie are set to commence retail operations next year-a sign of intensifying competition for affluent urban consumers in India.

Industry executives said more brands are likely to rush in, as demand in several global markets plateaus.

Last month, British brand Lush...