{\em Coinductive} characterizations of various {\em observational congruences}
which arise in the semantics of $\lambda$-calculus, when $\lambda$-terms are
evaluated according to various reduction strategies, are discussed. 
We analyze and extend to {\em non-lazy strategies}, both deterministic and
non-deterministic, Howe's {\em congruence candidate method} for proving the
coincidence of the applicative (bisimulation) and the contextual equivalences.
This {\em purely syntactical} method is based itself on a {\em coinductive}
argument.