ABSTRACT Objective: to understand spontaneous, scheduled and suppressed demands in the face of health needs and accessibility, from the perspective of Family Health Strategy professionals and users. Method: a qualitative study using Grounded Theory and Symbolic Interactionism, with 34 participants, 16 of whom are health professionals and 18 are users. The sources of evidence were open, intensive and individual interviews and memos. Data collection occurred between October/2016 to May/2017. Data analysis took place in interdependent steps: open, axial, selective coding, for the process. Results: thirty-two in vivo codes were indicated that represent the statement and meanings of the research participants regarding demand at Family Health Strategy, compiled in three theoretical codes that originated the central category “The Theory of Demand at Family Health Strategy: spontaneous, scheduled or suppressed?”. Spontaneous demand turns to complaints and illness, in daily appointments without previous scheduling, with restricted hours and as a means of accessing the health service. Scheduled demand is established in scheduling medical appointments for specific groups. Suppressed demand, more and more frequent in the daily routine of health services, is associated with the lack of access and resolution. Conclusion: health demands are configured in a space of lack of access and accessibility, denoting the main problem experienced by FHS users and professionals.