The Cauchy problem for a parabolic system of integro-dierential equations with an operator of Volterra-Fredholm type is considered. A fundamental matrix of solutions of the problem in classical Holder spaces is constructed, the estimates for the matrix and its derivatives are established. This makes it possible to prove the correctness theorem.

Se considera problema Cauchy pentru un sistem parabolic de ecua tii integro diferen tiale cu un operator de tip Volterra-Fredholm. Se construie ste o matrice fundamentala a solu tiilor problemei in spa tiile clasice Holder, sunt stabilite estimarile pentru matrice si derivatele ei. Acest lucru face posibila demonstrarea teoremei corectitudinii.