Update 1.10pm: Aldi have released a statement following the ruling.
It said: "While Aldi is pleased that the Court of Appeal upheld the High Court’s decision that Dunnes Stores had infringed Aldi’s trademarks, it is very disappointed by the overall decision and is considering an appeal to the Supreme Court.
"Aldi has always been in favour of clear and fair comparative advertising and indeed engages in it to highlight the outstanding value and quality that Aldi offers. This promise has been central to Aldi being the fastest growing retailer in Ireland for most of the last 10 years. However, it is important that any advertising is lawful and clear to customers.
"Aldi took this case against Dunnes Stores only after receiving no response to formal complaints made to Dunnes about its campaigns over a two-year period."
Earlier: There will be no High Court re-trial of the Aldi versus Dunnes Stores price comparison trademark infringement case, the Court of Appeal has ruled, writes Ann O'Loughlin.
However, Aldi says it wants to appeal to the Supreme Court last month's appeal court decision setting aside a 2015 High Court finding of trademark infringement through the use of shelf-edge labelling.
That was because this labelling had failed to objectively compare one or more of the relevant and verifiable features of the Dunnes' products with those of Aldi.
Aldi alleged Dunnes was in breach of the Consumer Protection Act 2007 and the European Communities (Misleading and Comparative Advertising) Regulations 2007.
At the heart of the appeal was whether the summer 2013 price advertising campaign by Dunnes, which employed Aldi's trademarks for identification and comparison purposes, complied with conditions imposed by the regulations when such advertising is carried out.
The appeal court disagreed with the High Court in relation to its finding that the shelf-edge labelling part of the campaign breached the regulations.
The three-judge appeal court, earlier this month, heard both sides on whether there should be a re-trial of the case and on the matter of costs.
Today, the court ruled there should be not re-trial because of the period of time since the issue at the centre of the case occurred.
President of the court, Mr Justice Sean Ryan, said this was also because the price comparison campaign was "long over", the test applied by the High Court (for establishing infringement) was the one put forward by Aldi and because a re-hearing would therefore be "significantly different" from what was before the High Court. No useful purpose would be served by a retrial, he said.
In relation to costs, the judge said the court would allow Aldi 20% as its trademark rights had been vindicated in the appeal court judgment.
However, Aldi would have to pay 80% of the costs as Dunnes was the "principal victor" in the appeal.
John Gleeson SC, for Aldi, asked for a stay on the costs order pending an application to the Supreme Court for leave to appeal the case.
Dermot Gleeson SC, for Dunnes, said there was no warrant for a stay. The only surprise was that Dunne hadn't mention the Court of Human Rights, he said.
Mr Justice Ryan granted a stay on the costs order providing an application for leave to appeal to the Supreme Court was lodged in four weeks. If the Supreme allows an appeal to be heard the stay would remain in place until its determination.
In its judgment on the matter, the appeal court said the High Court erred in its application of the rules of comparative advertising in the 2007 regulations
However, the appeal court agreed with the High Court finding that shop-floor advertising banners were not permissible because they did not constitute comparative advertising.