Top seed Angelique Kerber beat fellow German Mona Barthel 6-4 6-3 in the second round of the Dubai Duty Free Tennis Championships.
Kerber was joined in progressing by Russia's Ekeaterina Makarova, who beat Slovakian third seed Dominika Cibulkova 6-2 4-6 6-2 in two hours 10 minutes.
Second seed Karolina Pliskova of Czech Republic was also beaten, defeated 6-2 6-4 by Kristina Mladenovic of France.
Fourth seed Agnieszka Radwanska of Poland advanced with a 6-3 6-2 win over qualifier Elise Mertens of Belgium.
Other winners included Garbine Muguruza, Elina Svitolina, Samantha Stosur and Elena Vesnina.
Hungary Ladies Open third seed Julia Goerges of Germany beat Estonian qualifier Anett Kontaveit 6-7 (3/7) 6-3 6-4 in Budapest.
Qualifiers Anna Blinkova of Russia and Tamara Korpatsch of Germany recorded wins over Naomi Broady and Evgenita Rodina, respectively.
Wildcard Fanny Stollar of Hungary beat Danka Kovinic of Montenegro 6-2 7-6 (7/4) in the day's other match.
