A nonlinear L-1-control problem, which deals with the rejection of persistent bounded disturbances for nonlinear systems, is investigated in this paper. The concept of invariance plays an important role in the L-1-performance analysis and synthesis; the main idea is to construct an invariant subset in the state space such that achieving disturbance rejection is equivalent to restricting the state dynamics to the subset. The relation between the L-1-control of a continuous-time system and the l(1)-control of its Euler approximated discrete-time system is established.