For a wide class of triangular nonlinear control systems, sufficient conditions for the solvability of the observer design problem are established. The state estimation is exhibited by means of a Luenberger-type observer whose dynamics are in general time-varying and noncausal. The proof of our main result is based on a Lyapunov-like forwarding procedure which extends the methodology employed in previous works towards solvability of the same problem for a subclass of triangular systems with no inputs.