Many researchers note a nonlinearity of flow in tight rock samples at low rates. The effects include changes in apparent permeability with pore pressure gradient and so-called threshold gradients, below which low flow or no flow occurs. It is believed that these effects may be related to the influence of adhesive layers with altered properties at the interfaces between liquid and solid phases. For low-permeable rocks, the estimation of reservoir permeability without taking into account the nonlinearity of the flow can lead to significant errors. An account of the flow nonlinearity also can downgrade the reservoir productivity estimation and may result in underestimation of stationary oil zone appearances. Conventional methods for studying fluid flows in porous rocks are poorly suited for studying their permeability when approaching zero flow rates because of the lack of accuracy. Such studies also require a special approach for the interpretation of the data obtained. At the same time, there is a lack of discussion of the appropriate experimental technique in the publications known. Our goal was to develop a technique suitable for studying the flow nonlinearity at extremely low flow rates. Using the developed experimental technique, we carried out three series of consecutive tests on three similar limestone core samples. The samples were taken from the aquifer; however, their porosity and permeability are similar to the typical parameters of a tight oil reservoir. During the test series, we observed the change in the deviation from the linear Darcy’s law over a long time. We realized that in the sample with the most pronounced deviation from linear flow, there was a most significant decrease in net permeability in the entire series. We believe that our method can provide more precise evaluation of the permeability of tight rocks at the near real flow rate.