Novak Djokovic marked his first appearance at Queen's since 2010 with a comfortable opening win over Australian qualifier John Millman.
The 12-time Grand Slam champion, 31, eased to a 6-2 6-1 victory at the Fever-Tree Championships.
The Serb will face second seed Grigor Dimitrov in the last 16 after the Bulgarian won Dimitrov won 6-3 6-7 (4-7) 6-3 against Bosnian Damir Dzumhur.
Andy Murray and Kyle Edmund are also in action at Queen's Club on Tuesday.
South African third seed Kevin Anderson lost in three sets to unseeded Argentine Leonardo Mayer, while former Wimbledon finalist Milos Raonic led 6-1 3-1 when opponent Yuki Bhambri retired.