It is known that traditional approaches to calculating the characteristics of various fluids and systems in oil and gas production are based on the assumption of equilibrium of the process. On this basis, methods for calculating and designing various technological processes for oil and gas industry and pipeline transport were developed and created, which are now also finding successful practical application. But at the same time, a number of technological processes in oil and gas industry that are formed in a multiphase state and the results of viscometric studies show that when various structured systems move, flow instability occurs long before the Reynolds number reaches its critical value. This may be due, in particular, to the breaking up of relaxation properties in these systems, which, in addition to quantitative ones, can also lead to qualitative changes during their movement. The work investigated the rheological characteristics of oil-based drilling fluids of various compositions. Analysis of the results of these studies showed their nonlinear nature, which can be explained by structural changes. Based on rheological modeling, an attempt was made to diagnose the loss of structural stability of flows of multiphase oil-based drilling fluids. The work also proposed a dependence, which in the case of structure-forming multiphase drilling fluids allows one to estimate the time of structural relaxation, i.e. the time that corresponds to the beginning of the loss of structural stability of their flows during the drilling of wells