Abstract: The invention concerns a method whereby a fluid sample is brought (1) at constant pressure Pe and temperature maintaining the heavy fractions, in particular asphaltenes, in dissolved state and/or in stable colloidal state, at the intake (4) of a capillary passage with high pressure drop. Said sample is forced to flow through the capillary conduit, at an increasing flow rate. The method consists in measuring (11) the fluid pressure Ps and the fluid flow rate D (12) at the outlet (5) of the capillary conduit and in representing the variation curve of the quantity &Dgr;P=Pe−Ps or the quantity D as a function of the other quantity or as a function of time. The deposit pressure, characteristic of the threshold of deposit of heavy fractions, is defined as the value of pressure Ps, which corresponds to a change of the slope in the variation curve of the quantity &Dgr;P or the quantity D.