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Applying for such a card is relatively easy and should present no obstacle. You need the required documents, a passport and a little patience on the cantonal migration or the person Registration Office of the respective municipality.
Since the Schengen Agreement there is, in addition, a change concerning the kind of the foreign identity card for people not belonging to the European Union (EU) or the European free trade association (EFTA), namely the biometric foreign identity card.
All the answers and also around the topic of foreigner’s identity card can be found on the homepages of the respective cantonal Migration Office and here.