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I just wonder what the model# could be for this instrument and approximately which years it was available new?

The Cerveny F tuba you are showing is the CFB 651-4. It has the main tuning slide going vertical like the squat CFB 653 series. Those are the better playing Cerveny F tubas and I once read in The Tuba Journal the CFB 651 series you have was the beginning inspiration for the early B&S F tubas. The CFB 641 series has the main tuning slide going sideways and plays very out of tune.
If your tuba is engraved Amati, it would be model AFB 651-4

Matt Walters wrote:The Cerveny F tuba you are showing is the CFB 651-4. It has the main tuning slide going vertical like the squat CFB 653 series. Those are the better playing Cerveny F tubas...

Hmm- Those? Do you mean CFB651 is better, or CFB653 is better?

Ulli, not a native speaker... who looks for a F Tuba

CFB651 and CFB653 are both good. The 653 is shorter.

Matt Walters wrote:...The Cerveny F tuba you are showing is the CFB 651-4...
...If your tuba is engraved Amati, it would be model AFB 651-4...

Thank you for the information, greatly appreciated
Now, do you happen to know approximately between which years that model was current?

Thank you very much Dale, great info