Trade balances and unit values in Hungarian and Slovenian bilateral agri-food trade with Austria, Germany and Italy, respectively, to distinguish types of the one-way and the two-way trade flows, categories of price competition and categories of quality competition in the twoway trade flows, their dynamics and stability over time are analyzed. The two-way matched trade flows prevail among trade types. In the matched two-way bilateral agri-food trade there is prevalence of categories of price competition over categories of non-price competition, but varies across trading partners. In Hungarian agri-food trade the first category of successful price competition and the third category of successful non-price or quality competition prevail, suggesting comparative advantages for Hungarian agri-food products vis-a-vis bilateral trading partners. In Slovenian agri-food trade the prevalence is on the second category of non-successful price competition and on the fourth category of non-successful quality competition suggesting comparative trade disadvantages vis-à-vis bilateral trading partners. Looking dynamically, we did not find comparative catch up as for Hungary both successful price and successful non-price competition increased only with Austria, but deteriorate with Germany and Italy. For Slovenia, successful price and successful non-price competition remains at similar level with Austria, but similar as for Hungary, they declined with Germany and Italy. The probability of remaining the one-way trade is greater than the probability to stay within the same competition category in the two-way matched trade. While there are differences across countries, products, and over individual years, the mobility indices indicate the decline in mobility in trade flows. If these patterns continue, then more stable trade patterns are expected.