The article analyses the modern state of studies of economic behaviour of households in the world and Ukraine. It justifies the use of means and methods of mathematic modelling for the study of economic behaviour of these economic agents, capable of self-development and self-organisation in the process of endogenous or exogenous interaction. The article offers to use such a mathematical mechanism as the theory of ordinary differential equations as the most convenient and efficient instrument of study of behavioural dynamics not only at the stage of model construction, but also at the stage of conducting computational experiments. The article starts a cycle of the author’s works on issues of mathematical modelling economic behaviour of households not only as separate economic agents, but also as stable or situational conglomerations. One of the directions of further studies is the search for possibilities of building up fundamental solutions of differential equations in partial derivatives, which describe different aspects of economic behaviour of households.