Australian Open champion Angelique Kerber and two-time Wimbledon winner Petra Kvitova advanced in straight sets at the Aegon Classic in Birmingham.
German second seed Kerber saw off Shuai Peng 7-6 (7-3) 6-3, while Kvitova beat fellow Czech Lucie Safarova 6-3 6-2.
Britain's Tara Moore was one set all against Tamira Paszek, with compatriot Naomi Broady leading Daria Gavrilova 6-4 2-4, when rain intervened.
In Mallorca, French Open winner Garbine Muguruza lost in the first round.
The Spaniard was the top seed at the event which is making its debut on the calendar this year, but lost 6-3 6-4 to Belgium's Kirsten Flipkens in her first match since beating Serena Williams in the Roland Garros final on 4 June.
The weather in Birmingham prevented British number one Johanna Konta playing her first-round meeting with Japan's Misaki Doi. Their match is third on court in Wednesday's order of play.
British number three Broady will play Kerber in the second round if she overcomes Australian Gavrilova.
Moore, who reached the final of the Nottingham event last week, would face American seventh seed Madison Keys next.