Top seed Dominic Thiem secured his place in the quarter-finals of the Lyon Open with a straight-sets win over Spain's Roberto Carballes Baena.
Austrian Thiem, the world number number eight, progressed 6-2 6-4 and will next meet Guillermo Garcia-Lopez.
The Spaniard came through his second round match 7-6 (7/4) 6-3 against Calvin Hemery of France.
In Tuesday's first round games, Taylor Harry Fritz set up a clash against fellow American Jack Sock, the number three seed, as he defeated Matthew Ebden of Australia 6-4 6-2.
Portugal's Joao Sousa is out after he was beaten 6-4 3-6 6-4 by Slovak Filip Horansky, while Mikhail Kukushkin of Kazakhstan defeated home player Gregoire Barrere 6-2 6-3.
At the Geneva Open, Peter Gojowczyk defeated fourth-seeded Spaniard David Ferrer, the German winning 6-2 6-4 to book a place in the quarter-finals.
Number five seed Albert Ramos-Vinolas is also out after the Spaniard lost 6-1 6-2 against Hungary's Marton Fucsovics in the first round.
There was also disappointment for Jiri Vesely, the world number 79. Qualifier Lukas Rosol came through the battle of the Czechs, winning 2-6 7-6 (8/6) 7-6 (7/4) in just over two and a quarter hours on court.
Sixth seed Steve Johnson, though, had little problem as the American world number 47 progressed 7-6 (7/4) 6-3 against Marius Copil of Romania.
Italy's Andreas Seppi, the seventh seed, will have to finish his second round match against 21-year-old Bernabe Zapata Miralles on Wednesday because of rain. Seppi leads 7-5 3-2.
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