We study the behaviour of the solutions of boundary value conjugation problems for high order elliptic equations in variable domains $(\Omega_t,G^\prime_t)$ $(0 < t\leq 1)$ which depend smoothly on a parameter t in Krein’s sense. Considering the domain $$ as the limit of domains $(\Omega_0,G_0^\prime)$ when$t$ tends 0, we prove the existence and the uniqueness of the solution of the boundary value conjugation problem in $(\Omega_0,G_0^\prime).$