Mikael Ymer is the first out of the Swedes as he faces the 66-ranked Frenchman Quentin Halys.
That match is played at 18.00 at the earliest and then follows Leo Borg's match against last year's winner Tommy Paul, USA.
Tuesday's matches in SVT:
Alex de Minaur, Australia – Benjamin Bonzi, France
Jiri Lehecka, Czech Republic – Grigor Dimitrov, Bulgaria
Quentin Halys, France –
Mikael Ymer, Sweden
Leo Borg, Sweden
– Tommy Paul, USA