A court official identified suspects Amado Fakhre, a British citizen of Lebanese origin who was executive director of Coral Capital Group, and fellow Briton Stephen Purvis, the investment firm's chief of operations.
A half-dozen Cubans were also being tried in the case.
Coral Capital partnered with government entities on hotel management and represented automobile companies in Cuba until it was shuttered in 2011.
Purvis was seen entering a Havana building that houses a special tribunal Thursday morning, wearing a checkered shirt and escorted by an apparent state security agent.
He did not speak to reporters. The Cuban government did not comment on the case or allow media access to the proceedings.
Automobiles with license plates identifying them as belonging to the British Embassy in Havana suggested that U.K. diplomats were on hand to observe.
Canadian businessman Sarkis Yacoubian, president of another company, Tri-Star Caribbean, went on trial last week in the same courthouse on reported charges of bribery, tax evasion and "activities damaging to the economy."
No verdict has been issued in Yacoubian's case.
Another Canadian man, Cy Tokmakjian of the Tokmakjian Group, is also expected to go on trial shortly.