Issues in the mathematical semantics of two restrictions of the
$\lambda$-calculus, i.e. $\lambda I$-calculus and $\lambda_{V}$-calculus, are
discussed. A {\it fully abstract} model for the natural evaluation of the former
is defined using complete partial orders and strict Scott-continuous functions. 
A correct, albeit non-{\it fully abstract}, model for the SECD evaluation of the
latter is defined using Girard's coherence spaces and stable functions. These
results are used to illustrate the interest of the analysis of the {\it fine
structure} of mathematical models of programming languages.