Abstract. The paper is devoted to solving the problem of co-integration between Ukraine and the Republic of Moldova in the context of foreign trade. The study of co-integration makes it possible to determine common trends in the development of foreign trade and, based on the analysis of the dynamics of the development of one country, to forecast the development of foreign trade in another country. The study of the main indicators of foreign trade was carried out: volumes of exports, imports, trade balance. The share of export-import operations with the EU in the total volume of foreign trade of Ukraine and Moldova was chosen as the studied indicator. The article proposes to consider cointegrations both between long-term trends, which characterize the trend of foreign trade development, and between short-term trends, which reflect the cyclical component. A co-integration research mechanism has been developed, which includes three blocks: a block of analysis of literary sources, a block of mathematical tools, and a block of applied use. The use of decomposition models, trend models, spectral analysis, orthogonality indicators and pairwise correlations is proposed as a mathematical toolkit. Using the Foster-Stewart method, an analysis of the presence of a trend in the variance and average was carried out. The above calculations showed the presence of a trend and cyclical component, which allowed the use of additive decomposition models. For the study of long-term trends, a linear trend model was chosen for both Moldova and Ukraine. A spectral analysis of the cyclic component was carried out, which made it possible to identify five main harmonics with a unique frequency and amplitude. The combination of these harmonics caused 95.8% and 90.4% of the cyclical component for Moldova and Ukraine, respectively. An analysis of cointegration between short-term and long-term trend functions was conducted, which revealed medium cointegration in the long-term trend and high cointegration in the short-term trend. The cointegration analysis of the indicator values proved a high degree of cointegration for both long-term and short-term trends.