Welsh Liberal Democrat leader Kirsty Williams said orthopaedic patients at a hospital in Bridgend have to wait more than 70 weeks for elective surgery.
Also, Plaid Cymru leader Leanne Wood said 123 children are waiting more than 36 weeks for paediatric treatment.
Under Welsh government targets, 95% of patients should start treatment within 26 weeks of being referred.
Every patient's treatment should start within 36 weeks of referral.
At First Minister's Questions on Tuesday, Ms Williams referred to a letter from a manager at Princess of Wales Hospital which says "unscheduled care pressures" between December 2014 and April 2015 led to elective surgery being "curtailed".
Karl Murray, interim service director at the hospital, wrote that, as a result, waiting times for things like hip and knee operations have risen to "in excess of" 70 weeks.
Carwyn Jones said he was happy to "investigate the circumstances regarding her constituent's complaint" but increasing demand for operations was a problem across the UK.
The Welsh government said it has made it clear to Abertawe Bro Morgannwg University Health Board that it expects to see improvements in waiting times.
Ms Wood asked the first minister to ensure "not a single child is waiting longer than 36 weeks for paediatric surgery" by the end of the year, as she said was the case three-and-a-half years ago.
Mr Jones replied: "I can certainly give my commitment to ensuring that that figure drops. We want to ensure the waiting times continue to be driven downwards.
"We expect to see an improvement in referral to treatment times."
NHS waiting times should improve after delays for certain treatments, first minister Carwyn Jones has said.