The first deals on Monday were only in five stock index certificates as the exchange has no company listing yet.
Its first initial public offering is expected to come next month when the Lebanese telecommunications firm, Investcom, is listed.
The chairman of the exchange, Lynton Jones, said he hopes to have 15 to 20 firms listing in the next 18 months.
They are expected to come from the Middle East, the Indian subcontinent, China, South Africa and Eastern Europe.
Filling the blank
Located in a steel-and-glass building like the Arc de Triomphe, the Dubai exchange is intended to fill a blank space in the trading day.
Currently market activity begins in Asia and jumps over the Middle East to resume in exchanges in Europe and North America.
"We believe the DIFX fills a vacuum by creating an exchange in the heart of one of the world's most dynamic and fastest-growing economies"
Mukhtar Hussein, head, HSBC's Middle East investment banking
"We believe the DIFX fills a vacuum by creating an exchange in the heart of one of the world's most dynamic and fastest-growing economies," said Mukhtar Hussein, HSBC Bank's head of Middle East investment banking.
HSBC has signed on as one of four European member banks that will handle IPOs and other market duties.
Local stock markets, which tend to permit only residents to trade, are booming in the Middle East.
By contrast, the Dubai exchange is an international market that is open to foreign companies and foreign investors.
The exchange's operators say it will run under the same transparency and regulatory rules as the New York and London exchanges.
For now, the market will open Monday-Friday for only three hours a day, between 2pm and 5pm (1000 to 1300 GMT).