Three music companies say UPC Communications, the country's second-largest internet service provider (ISP), must be forced by court order to move against its subscribers who illegally download music and other copyrighted material.
The Irish companies of Sony Music, Warner Music and Universal Music want injunctions requiring UPC to apply rules to combat illegal downloading which have already been agreed with the largest ISP, Eircom.
The Commercial Court has begun hearing the three companies' application for injunctions against UPC.
The case, before Mr Justice Brian Cregan, is due to last up to eight days.
The court heard evidence had been provided of copyright infringement by UPC subscribers.
In the month of November 2013 alone, evidence of 7,757 infringements of copyright in a sample 250 sound recordings was provided to UPC, plus details of the infringing subscribers' internet addresses.
UPC was asked, but declined to adopt, a "three strikes and you're out" protocol being used by Eircom, under which infringers are warned twice about the consequences of infringement before a third step is taken to terminate their internet service contracts.
It is claimed that where this process was used, it had proven "remarkably effective".
UPC argues a graduated "three strikes" policy should be subject to legislation, as it involved the question of freedom of expression and the balancing of rights.
Opening the case for the music companies, Michael McDowell said a graduated response system is a reasonable and affordable measure for UPC.
UPC could come up with its own alternative graduated approach, whether it be "two strikes" or "five strikes", he said.
Mr McDowell said it was an "illusory remedy" to suggest illegal downloading through "peer-to-peer" file sharing could be dealt with by shutting down "Pirate Bay" type websites.
Mr McDowell said there were a number of agreed facts between his clients and UPC, including that the illegal downloading was taking place and that its internet service was being use to facilitate wholesafe theft.
Cian Ferriter, for UPC, said his client had no difficulty in handing over information, subject to court order, which the music companies can then pursue - but what was actually being sought was that UPC set up an "entire system" to deal with this issue itself.