Police in Edinburgh were last night appealing to Hogmanay crowds who may have witnessed a sexual assault on a 21-year-old woman in the Canongate area of the Royal Mile between midnight and 2.30am.
A woman was also attacked near Aviemore's Vault nightclub in the early hours yesterday.
The suspect in the Edinburgh assault is described as white, in his late teens or early 20s, medium to heavy build with dark spiky hair with a noticeable gap between his front teeth.
Yesterday police cordoned off parts of the cemetery of Canon-gate Kirk, as officers wearing white suits searched the area.
DI Alyson Brown said: "The Canongate would have been busy with members of the public out celebrating Hogmanay and we are particularly interested in speaking to revellers or locals who were in the area after midnight and remember seeing or hearing anything suspicious.
"I would urge anyone who recognises the description of the suspect to come forward."
The attack in Aviemore took place at around 1.30am in the area known as 'the tunnel', and Police Scotland want to speak to people who may have been in the area at the time.
Hogmanay was the busiest night of the year for the nation's ambulance service which dealt with more than 2400 calls to its 999 centres across Scotland.
The Scottish Ambulance Service dealt with 2423 calls - but that number was 15% lower than the total of 2878 in 2012.
In total ambulance crews attended 1280 incidents, also a lower figure than the 1364 incidents to which they responded in 2012.
Additional call handlers, dispatchers and ambulance crews were on duty to deal with the surge in demand across the country.
Edinburgh was the busiest of the three Ambulance Control Centres, although yesterday Lothian NHS said that A&E admissions were not unusually high.
Greater Glasgow and Clyde Health Board said that the A&E departments at the city's Royal and Western infirmaries were "busier than usual" but the increase in activity had been expected.
Between midnight and 7am, demand for ambulances was particularly high, with ambulance control rooms dealing with 1864 calls and dispatching ambulance crews to 923 incidents.
Pauline Howie, chief executive of the Scottish Ambulance Service said: "Hogmanay is always our busiest night and this year was no different as we dealt with a high volume of calls across the country.
"Whilst there were fewer calls overall than last year, the number of incident responses was similar and activity at times was intense, with most of the workload between midnight and 7am."
Chief Superintendent Mark Williams, Police Scotland Edinburgh Commander, said the Hogmanay celebrations had been a success overall. Preliminary figures show there were five arrests for minor disorder.
CS Williams said: "Edinburgh's Hogmanay celebrations have once again proven to be a major success."