We define a minimal operator L0 generated by an integral equation with an operator measure and prove necessary and sufficient conditions for the operator L0 to be densely defined. In general, L 0 is a linear relation. We give a description of L 0 and establish that there exists a one-to-one correspondence between relations bL with the property L0 ⊂ bL⊂L 0 and relations  entering in boundary conditions. In this case we denote bL = L. We establish conditions under which linear relations L and  together have the following properties: a linear relation (l.r) is self-adjoint; l.r is closed; l.r is invertible, i.e., the inverse relation is an operator; l.r has the finitedimensional kernel; l.r is well-defined; the range of l.r is closed; the range of l.r is a closed subspace of the finite codimension; the range of l.r coincides with the space wholly; l.r is continuously invertible. We describe the spectrum of L and prove that families of linear relations L() and () are holomorphic together.