In the paper nonlinear, finite-dimensional, continuous-time dynamical systems with constant coefficients are considered. It is generally assumed that the systems have many inputs and many outputs. The main purpose of the paper is to propose a new design procedure for a nonlinear observer which allows one to estimate both the state of the system and the unknown input. Using the theory of ordinary differential equations and certain methods taken directly from control theory, sufficient conditions for asymptotic convergence of the estimation error are formulated and proved. A simple numerical illustrative example is also given. Moreover, many remarks and comments on nonlinear observer design problems are presented. Finally, it should be pointed out, that similar problems have been considered in the paper [F. Zhu
and Z. Han
, IEEE Trans. Autom. Control 47, No. 10, 1751–1754 (2002)].