using TLS (>1.2) with more than one certificate

[Tobias.Wolf at t-systems.com]

I've a server application and need to support RSA and ECC clients at the same time.
I don't know which certificate from my local keystore I have to send to the client, btw I have a rsa and a ecc certificate in my keystore already.
I don't know with which certificate (rsa or ecc) a client comes during handshake of a tls connection.
How can this technically work?

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