A slate of 16 matches had been scheduled for Monday in one of the few grass-court tournaments before Wimbledon begins June 25 but the weather led to all being pushed back.
Organizers put together a schedule of 24 matches for Tuesday at the Queen's Club in London.
Defending champion Andy Murray is the top seed for the tournament, which features Top 10 players Jo-Wilfried Tsonga, who lost in the finals to Murray last year, and Janko Tipsarevic. The eight top seeds were all given first-round byes.
The $785,000 event has its singles final scheduled for Sunday