This paper considers the solution of a multi-objective optimisation problem using adaptive extremum-seeking control for a class of uncertain nonlinear systems. It is assumed that the equations describing the dynamics of the nonlinear system and the cost functions to be optimised are unknown and that the objective functions are measured. The proposed extremum-seeking control technique uses a time-varying estimation of the unknown gradients that minimises the impact of the choice of dither signal on the performance of the extremum-seeking control system. The technique guarantees convergence of the system to any point of the set of Pareto optimal solutions. It is adapted to allow the computation of specific desirable Pareto solutions using a utopic formulation. Simulation examples are used to illustrate the effectiveness of the proposed technique.