Almost a quarter said they would not apply for their own job and there were complaints about "burn-out".
The report by the Headteachers' Association of Scotland, which coincidentally appeared just before national stress awareness day on Wednesday, said the job-sizing mechanism created under the agreement was seen as a major contributory factor to the pressures faced by heads and deputes.
The survey had a response rate of just 204 from 600 questionnaires sent to HAS members. This represents only around 12 per cent of the 1,759 secondary heads and deputes recorded as being in post at the last census.
Despite this, Bill McGregor, general secretary of the HAS, warned: "The picture that emerges reinforces the current trends of reduced applicants for headteacher and depute head posts."
Mr McGregor said the Scottish Executive's drive to improve school leadership could be put at risk unless urgent steps were taken to improve the work-life balance of senior school managers.
Lindsay Roy, the association's president, said that on average heads and deputes were working 58 hours a week, not including extra-curricular activities or attending parent evenings, school concerts and similar events. Mr Roy was particularly concerned that 54 per cent of respondents said their job was having an adverse effect on their health.
More than 60 per cent said demanding and confrontational parents, dealing with raised expectations of staff and managing pupil behaviour were particularly stressful. There were also tensions between the "reactive and strategic" roles of heads and deputes.
Between 30 per cent and 60 per cent cited pressures from their authority, weekend working, the pressure for continuous improvement, the expectation of being constantly available to everyone and "competing accountabilities".
A strong theme running through the survey is the feeling that the national agreement has benefited teachers but shifted the load on to senior management. The report said there was "less flexibility among staff who focus more on the 35-hour week" and that "conditions of the general teaching staff have increased at the expense of senior management teams".
Asked if they would apply for their own job, 77 per cent of respondents (a figure which included a higher proportion of heads) said they would; 23 per cent (a higher proportion being deputes) would not.
Ronnie Smith, general secretary of the Educational Institute of Scotland, said the union shared some of the HAS's concerns, such as the impact of management restructuring.
"We recognise as well the point they make about heightened demands or expectations that now sit on the shoulders of headteachers," Mr Smith said.
"But the point that they have lost responsibility and power but have more accountability is not unique to headteachers."
Ewan Aitken, education spokesperson for the local authorities, pointed out that there is to be a review of the teachers' agreement next year when the views of all the groups involved would be taken into account. "We provide a high level of support for our headteachers at present, both in terms of work-life balance and administrative support. Business managers are one example of that," Mr Aitken said.
"We are always concerned about the health and well-being of our staff but I am convinced that their participation in the 2006 review will provide them with the answers they need."
A spokeswoman for the Executive said: "We do recognise the difficult job that headteachers, deputes and teachers have to do. But we think the introduction of the 35-hour week, the introduction of extra support staff and the reduction in class contact time have all been very beneficial."
A workload audit was being undertaken by the Scottish Negotiating Committee for Teachers (SNCT) which would consider issues affecting heads as well as other teachers