The role played by coercive inequalities in the study of local boundary‐value problems for parabolic and elliptic differential equations is well known ( see, e.g.,[14],[21]). In present paper we consider the nonlocal boundary‐value problems for parabolic and elliptic differential equations. The coercive inequalities for the solution of these nonlocal boundary‐value problems are presented. © 2004 American Institute of Physics