Guy Parmelin's successor on the Federal Council must be chosen by December, with the UDC under pressure to put forward a woman for only the second time in a quarter-century
Parmelin will step down on 31 December after eleven years in government.
UDC candidates have until 23 October to declare, with the party's nomination due 20 November and Parliament voting on 9 December.
Names already circulating include Geneva's Céline Amaudruz, St Gallen senator Esther Friedli, Zurich health minister Natalie Rickli, and Romand MPs Yvan Pahud and Nicolas Kolly.
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