Yes, non-resident Indians (NRIs) can open two different kinds of Demat accounts. These are accounts that are designated as Non-Resident Ordinary (NRO) or Non-Resident External (NRE) demat.
With the former, foreign nationals can purchase and sell stocks, bonds, and mutual funds in India. It is a fully repatriable Demat account. NRIs can open an NRO Demat Account to trade and invest in stocks, futures, and options.