Finite-time and infinite-time tracking properties are defined. They raise new tracking problems studied in the framework of time-invariant continuous-time linear multiple-input multiple-output (MIMO) systems with a state-space description. New system and control concepts are introduced and defined: the finite-time and infinite-timenatural trackabilityconcepts, and that ofelementwise exponential tracking.The necessary conditions and sufficient conditions are proved for these concepts. The problem of synthesizing an appropriate control to be called the natural tracking control will be solved via high-gain PI natural tracking control. It guarantees either finite-time or infinite-time elementwise exponential tracking. The high-gain natural tracking controller is synthesized with the knowledge of the system transfer matrix function with respect to the control, and this is the only information required about the system in order to design the controller. Knowledge or measurement of the system internal states and system external disturbances is also not required. Several illustrative examples demonstrate these concepts