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Background The acute out-of-hours healthcare services are challenged by increasing demand in many countries. We aimed to examine factors influencing the intended help-seeking in out-of-hours care for acute health problems during evenings, nights, and weekends. Methods We conducted a survey study based on data from parents of children (aged 0–4 years) and adults (aged 30–39 and 50–59 years) in Denmark, the Netherlands and Switzerland. Intended help-seeking behaviour was measured by six hypothetical case scenarios. We used Andersen’s Behavioural Model to categorise potentially influential factors and applied multiple binomial regression to assess the influence of selected factors. Results A total of 1015 parents and 2942 adults participated. We identified several significant influential factors. Parents holding a low education (OR 1.56), having migrant background (western: OR 1.23; non-western: OR 1.93), having one child (OR 1.24), perceiving few barriers to using out-of-hours primary care (OR 1.59), perceiving difficulties with organising childcare (OR 1.13), and having a history of frequent contacts with out-of-hours care (OR 1.55) were more inclined to contact out-of-hours care, whereas female (OR 0.85) and non-anxious parents (OR 0.77) were less inclined. Adults who were older (OR 1.01), holding a medical education (OR 1.13), having non-western background (OR 1.28), being unemployed (OR 1.17), perceiving few barriers to using out-of-hours primary care (OR 1.37), and having a history of frequent contacts with a GP (few: OR 1.15; more: OR 1.22) and/or with out-of-hours care (one: OR 1.20; more: OR 1.49) were more inclined to contact out-of-hours care, whereas adults with no or little social support (OR 0.84) and adults with high health literacy level on health information (OR 0.91) were less inclined. Dutch parents were less inclined than Danish parents to contact out-of-hours care (OR 0.62), whereas Swiss adults were more inclined than Danish adults to contact out-of-hours care (OR 1.16). Conclusion We identified several factors related to intended help-seeking in out-of-hours care. These results could be used to develop targeted interventions, but more research is needed to examine the underlying explanations for the identified differences. Electronic supplementary material The online version of this article (10.1186/s12889-018-6332-6) contains supplementary material, which is available to authorized users.