  Parametric Gr\"obner bases have been studied for more than 15 years and are
now a further developed subject. Here we propose a general study of parametric
standard bases, that is with local orders. We mainly focus on the commutative
case but we also treat the case of differential operators rings. We will be
concerned by two aspects: a theoretical aspect with existence theorems and a
practical aspect devoted to how we can explicitely compute such objects when
the given data are algebraic. We believe that parametric standard bases are
important for both aspects. From a theoretical point of view, they constitute a
strong tool for proving constructive results. From a practical one, they
provide a tool for studying explicitely local objects associated with
parametric algebraic ideals.
