We relate the existing first-order approaches for discrete- and continuous-time problems by considering continuous-time principal--agent problems as limiting cases of multi-period discrete-time formulations. Our multi-period discrete-time formulation gives an intuitive explanation of why the validity of the first-order approach to continuous-time formulation in Schattler and Sung (1993) can be more easily established. We also show that although continuous-time formulations are far easier to deal with, their solutions may not be, in general, as simple as the one in the Brownian model. Under slightly modified assumptions solutions typically depend on the entire history of the process, rather than only on the terminal state alone.