SSL Handshake failed - client certificate authentication and also without certificate

Janez, the clientssl profile would be very useful, as would be some clarifications on what you are trying to achieve. For example, are you looking for "client certificate authentication" if so have you configured the "client authentication" section of the clientssl profile? Does the application require the f5 to present a certificate to the application server, if so you'd need to add the Certificate in the "configuration" section. If the application needs to authenticate the client directly, then this setup might break that, and you would need to implement Proxy SSL. See ClientSSL Profile and ServerSSL Profile