Hospital grounds across Scotland became completely smoke-free yesterday.
The newly-adopted policy applies to the entrances and surrounding parts of all health centres and NHS buildings.
The Scottish Government has set the ambitious target of creating a tobacco-free generation by 2034.
Public Health Minister Maureen Watt last night welcomed the move and thanked health boards for setting an example.
Signs have been put in place to remind people of the new rules and smoking shelters have been closed off.
But when The Press and Journal visited the north-east’s flagship hospital yesterday afternoon, about six people were spotted with cigarettes in their hands.
Ricky Inkson, a chef from Bucksburn, said he was aware of the policy but had decided to smoke anyway.
The 25-year-old said: “It’s not going to be good for staff who want to smoke on their break, because they are going to have to travel further on their break, so the NHS might need to bring in longer break times.
“There’s plenty of smoking shelters so I don’t see why people can’t smoke there.”
Tobacco controller co-ordinator for the site, Derek Petrie, said it was important to view the policy in its full context.
He added: “We realise that for regular smokers this may be a challenge, but smoking kills 13,000 Scots every year.
“One thousand of these will be in Grampian, where there will be around 5,000 smoking-related hospital admissions with a potential annual cost of £46million – that’s preventable, so the NHS must lead by example.”
Ms Watt also encouraged people to respect the health of others.
The SNP MSP for Aberdeen South and North Kincardine added: “Hospitals are places where people go for rest, recuperation and recovery, and it’s quite right that they should be smoke-free.”
Elsewhere, the scheme has been in place at Raigmore Hospital in Inverness since February.
NHS Highland consultant breast surgeon, Nick Abbott, said: “Although this may have been a challenging policy for some to abide by, the long-term health benefits for staff, patients and visitors justify this approach.
“Support has been available for anyone who has found this difficult.”