Instability of fluid flow has long been linked with the eigenvalues of the Orr‐Sommerfeld equation. Recently, it has been shown that even though all eigenvalues may be stable, it is still possible to have disturbance growth. This is because the Orr‐Sommerfeld operator is non‐normal. We identify which eigenmodes are important in two‐dimensional disturbance growth. We find a relationship between maximum growth and growth caused by the adjoint of the leading eigenmode for both plane Poiseuille flow and plane Couette flow. The work points to a connection between the occurrence of the first degeneracy of the Orr‐Sommerfeld operator and the first appearance of disturbance growth. ©1996 American Institute of Physics.