Traveling with a residence card

I have heard that I can travel only if my residence card expires in 6 months. Is this true?

No, it is not true.

The Schengen Borders Code (Articles 6 and 8) stipulates only that a residence permit must be valid and that this must be checked.

It does not state that it must be valid for a specific time on the date of entry.

Article 6
Entry conditions for third-country nationals
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1 (b) they are in possession of a valid visa, if required pursuant to Council Regulation (EC) No 539/2001 ( 1 ), except where they hold a valid residence permit or a valid long-stay visa;
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Article 8
Border checks on persons
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3. thorough checks as follows:
(a) thorough checks on entry shall comprise verification of the conditions governing entry laid down in Article 6(1) and, where applicable, of documents authorising residence and the pursuit of a professional activity. This shall include a detailed examination covering the following aspects:
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(ii) verification that the travel document is accompanied, where applicable, by the requisite visa or residence permit;
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Sources:

• Schengen Borders Code
  • 2019-06-11 M3