Both sides presented closing arguments in a Californian state court for the first phase in a lawsuit between them.
According to Reuters, HP attorney Jeffrey Thomas said Oracle was obligated to support Itanium, but Oracle lawyer Dan Wall dismissed the claim.
He said that HP was using litigation to try to draw up a contract that was never agreed with Oracle.
Oracle stopped software development on Itanium last year, saying Intel made it clear that the architecture was nearing the end of its life.
HP claimed it had an agreement with Oracle that support for Itanium would continue. If Oracle did not back it then the hardware it made would become obsolete.
HP thinks that commitment was affirmed when it settled a lawsuit over Oracle's hiring of ousted HP chief executive Mark Hurd. It wants $4 billion in damages.
Santa Clara Superior Court Judge James Kleinberg will decide if there is a contract between HP and Oracle, and its terms.
If Kleinberg agrees with HP, then a jury will decide whether Oracle violated the contract, and damages.
Kleinberg has said that the case is similar to a divorce between the technology giants. He indicated he would not rule on the case before mid-July.