Turnover and profit at Rank's Hard Rock Café division both dropped during the six months to 30 June.
Turnover fell by 1.9% to £112.9m, down from £115.1m at the same point last year.
Profit dropped by 12.8% to £11.6m, from £13.3m last year.
Rank said it had seen increased like-for-like sales in its Hard Rock restaurants but at a lower profit margin. The contribution from Hard Rock's hotels had also fallen.
The group opened two new owned Hard Rocks during the six-month period, in Bristol and in Louisville, Kentucky.
New franchised cafés opened in Catania, Italy, in January, and in Dublin in June.
The extension of Hard Rock into non-restaurant activities continued with the opening of two hotel/casino developments in Florida. One of these includes a 500-bedroom hotel and the other a 250-bedroom hotel.
The new Hard Rock Hotel in New York is expected to open in early 2005.
Rank chief executive Mike Smith said most of the new growth for Hard Rock would come from franchises.
"We think there are major markets still for at least 50 more cafés, mostly franchise," he said.
Rank might eventually sell off its company-owned cafés to concentrate solely on franchise, Smith added.
The company also hopes to announce its first Hard Rock Hotel in Europe in the next few months.
Smith said the Hard Rock Casino in London was proving successful, but the one in Manchester was still not making money.
"We can get attendance but we don't get the spend per head," he said.
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