The Royal Cornwall Hospital Trust said it was overwhelmed over Easter and is struggling to discharge patients.
A ward closed at Truro's hospital on Monday because of an outbreak of Norovirus. People are being urged to avoid A&E unless absolutely necessary.
In February, the trust declared a "black alert" for about a week.
A black alert is the highest level of alert and means hospital services are unable to cope with demand.
Dr Andy Virr from the trust said there were some issues with the NHS 111 phone system during the weekend which prevented calls getting through to the Cornwall GP service, which caused delays.
That "led to people voting with their feet and coming to A&E" which meant some patients remained on trolleys for 10 or 11 hours and operations were cancelled, he said.
Debbie Pritchard, from patient group Healthwatch Cornwall, was not surprised the alert was declared.
"There is still a lot of confusion around what services people should access out of hours," she said.
The county's Clinical Commissioning Group (CCG), NHS Kernow, is now asking people to consider the most appropriate place to go for treatment when unwell.
Peter Stokes, deputy director of operations at the CCG, requested "relatives and friends be available to pick up people who have been inpatients and are ready to be discharged to free up beds".

Voyage of Time, Nocturnal Animals and Les Beaux Jours d'Aranjuez will vie with 17 others for the Golden Lion.
Also included as official selections are Pablo Larrain's Kennedy biopic, Jackie, and Ana Lily Amirpour's cannibal love story, The Bad Batch.
The event opens with Damien Chazelle's musical La La Land on 31 August.
Malick's Voyage Of Time, which he has worked on for over three decades, is an exploration of life on Earth narrated across two edits by Brad Pitt and Cate Blanchett.
Wenders has previously won the Golden Lion for his 1982 film The State of Things and headed the festival's jury in 2008.
Both his film and Ford's Nocturnal Animals are screen adaptations of written works - the former based on Peter Handke's play Die schÃ¶nen Tage von Aranjuez and the latter being based on Austin Wright's novel Tony and Susan.
Also included in the official selections are Sicario director Daniel Villeneuve's sci-fi drama Arrival; Derek Gianfrance's story of a lighthouse keeper, The Light Between Oceans; and films from directing duos Massimo d'Anolfi and Martina Parenti and Mariano Cohn and Gaston Duprat.
British director Sam Mendes will head the jury at this year's festival.
Away from the Golden Lion competition, the festival will also debut Nick Hamm's film about the unlikely friendship between the Reverend Ian Paisley and Martin McGuinness, The Journey, and Mel Gibson's Hacksaw Ridge, which tells the story of a World War Two conscientious objector.
The 73rd Venice International Film Festival will close on 10 September with a showing of Antoine Fuqua's remake of The Magnificent Seven.
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A hospital trust in Cornwall has declared a "black alert" for the second time this year due to "extreme" pressure on its services.
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New works from directors Terrence Malick, Wim Wenders and Tom Ford will compete for the top prize at the Venice International Film Festival.