Women's world number one Aryna Sabalenka is through to the second round.
The Belarusian beat Carson Branstine of Canada in straight sets 6-1 7-5 to progress.
Two-time finalist Ons Jabeur was forced to retire injured in her first round match Bulgarian Viktoriya Tomova.
22nd seed Donna Vekić from Croatia and Ukrainian 13th seed Elina Svitolin won their matches in straight sets.
Defending men's singles champion Carlos Alcaraz is tied at two-sets-a-piece with Fabio Fognini in round one at Wimbledon.
Alcaraz leads 3-games-to-love in the fourth set.
American 12th seed Frances Tiafoe beat Elmer M�ller from Denmark in straight sets, 6-3 6-4 6-2.
Ninth seed from Russia, Daniil Medvedev was beaten in four sets by Frenchman Benjamin Bonzi having lost two tiebreaks in the match.
