General equations for the linear responses of inner- and outer-spool speed to change in turbine-inlet temperature and exhaust-nozzle area are derived and evaluated from hypothetical two-spool-engine characteristics at design speed. The resultant equations of response are corrobated with experimental data. At design speed the response of inner-spool speed to turbine-inlet temperature approximated a first-order lag specified by the time constant of the inner spool. The outer-spool speed to turbine-inlet temperature was found experimentally to be identical with the response of inner-spook speed, in that it approximated a first-order lag specified by the inner-spool time constnat. The analytically derived response of outer-spool speed to turbine-inlet temperature was a lead second-order lag that culd result in the experimentally determined response by cancellation of terms in the response equation. With respect to changes in exhaust-nozzle area, the design-speed response of the outer-spool speed approximated a first-order lag specified by the outer-spool speed approximated a firs-order lag specified by the outer-spool time constant, whereas the inner-spool speed response approximated a second-order lag, but of negligible amplitude.