Musical celebrations are feline problems (9)

I believe the answer is:

hairballs

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'feline problems' is the definition.
Although both the answer and definition are plural nouns, I cannot understand how one could define the other.

'musical celebrations' is the wordplay.
'musical' becomes 'hair' (b960s musical).
'celebrations' becomes 'balls' (I can't explain this - if you can you should believe this answer much more).
'hair'+'balls'='HAIRBALLS'

'are' acts as a link.

Can you help me to learn more?

I've seen this clue in The Daily Express.

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