In the first, the adjudicator supported Jarvis' case and Alstom paid £1.6m. In the second, Jarvis secured another £1.3m, but Alstom refused to pay it.
Jarvis Facilities therefore asked the Technology and Construction Court to enforce the award.
Alstom then hit back with its own writ disputing the substance of the adjudicator's decision, and claiming that Jarvis should repay £4m.
In a judgment delivered last week, the TCC rejected Jarvis claim for the enforcement.
This means that Alstom is no longer under an immediate obligation to pay Jarvis £1.3m, and it may be entitled to recover the £1.6m it handed over after the first adjudication.
However, the case cannot be resolved and no money can change hands until the court decides on the correct valuation of the disputed contract.
Alstom is seeking a declaration that the value of Jarvis Facilities' subcontract did not exceed £10.3m.
It is also seeking to recover £2.4m plus VAT, which it calculates is the amount in excess of the £10.3m that it has already paid Jarvis for its work on the project.
Both cases concern work to extend the Tyne and Wear Metro from Pelow to South Hylton via Sunderland. The work includes installing signalling and telecoms equipment and the renewal of existing signally equipment.
A legal source commented that the case could have important repercussions for adjudication as a method of dispute resolution in the future.
The process of adjudication, introduced by the 1996 Construction Act, is intended to provide a quick and cheap way to temporarily resolve disputes.