A quarter of patients had to wait more than four hours to be seen in the accident and emergency department at Scotland's flagship hospital.
NHS figures show that over the last week in April, the Queen Elizabeth University Hospital in Glasgow only managed to deal with 75% of A&E patients within the four-hour target waiting time.
Liberal Democrats said that was the worst performance since the £842 million facility opened in 2015.
The statistics show that in the week ending April 30, 91.3% of A&E patients across Scotland were seen and either admitted, transferred or discharged within four hours - below the Scottish Government's interim target of 95%.
There were 223 patients who spent more than eight hours in an emergency department, with 45 waiting more than 12 hours.
Across the NHS Forth Valley area, more than a fifth of A&E patients waited more than four hours, with 78.4% of cases dealt with in the target time.
Liberal Democrat health spokesman Alex Cole-Hamilton said: "It is clear from these new statistics that emergency departments across Scotland are really struggling to meet demand.
"At the Queen Elizabeth University Hospital alone almost 500 patients waited longer than four hours to be dealt with. It has struggled to meet this target from day one and staff and patients will be frustrated that there is little sign of this changing.
"The facilities and dedication of the staff at the QEUH are first class but, as the Royal College of Nursing warned last week, services are under 'real strain'.
"Instead of focusing on another divisive independence referendum, SNP ministers should tell staff and patients at this hospital and others on the front-line across Scotland when they will finally deliver the support and resources they so desperately need."
Scottish Labour health spokesman Anas Sarwar said: "These figures expose the impact of the SNP's mismanagement of the NHS.
"The Queen Elizabeth University Hospital cost £850 million and has been opened for two years now - these figures can't be dismissed as teething problems. SNP ministers must get a grip of this problem urgently.
"The SNP Government should focus on the day job of running the NHS rather than trying to force another divisive independence referendum on the people of Scotland."
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