In this paper, we consider nonlinear continuous-time Markov chains

with a finite state space. We define so-called *Q*-operators as an extension of

*Q*-matrices to a nonlinear setup, where the nonlinearity is due to parameter

uncertainty. The main result gives a full characterization of convex *Q*-operators

in terms of a positive maximum principle, a dual representation by means of *Q*-

matrices, continuous-time Markov chains under convex expectations and fully

nonlinear ODEs. This extends a well-known characterization of *Q*-matrices.