At least this gives you a high-faluting alternative.
You don't tell us what the hands (the one and the other) are actually doing on your first page, or what the contract is generally about.
But it sounds like some sort of preamble setting out the factual background on which the contract is based.

to drop the einer/andererseits would be a permissable omission.
To stress that there are no other parties involved you could say:
bilateral contract between xxx and xxx.

hope this helps

this is formal legalese and imho nothing much is lost by leaving it out, but is often seen and might suit your purpose

Solitamente nei contratti inglese esiste un "between" che lega le due parti dell'accordo.
Se fosse un atto giuridico, si dovrebbero tradurre con Plaintiff e Defendant, ma se dici che questo non è diritto processuale, bensì solo diritto commerciale, meglio un "between ...... and .......(the parties) it is agreed that" che è consueto nei contratti inglesi.

Guarda questo bellissimo e chiarissimo atto. Il sito è australiano, ma rispecchia il diritto vigente in Australia deriva da quello britannico.

Ciao

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Note added at 4 hrs 4 mins (2005-05-20 13:08:10 GMT)
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All in all *between the parties it is agreed* is highly sufficient. Or as an alternative you could put \"one party\" and \"the other party\" if the parties are only two. Unusual but correct. I think I happened to see one document like that.