  Tangential families are 1-parameter families of rays emanating tangentially
from smooth curves. We classify tangential family germs up to Left-Right
equivalence: we prove that there are two infinite series and four sporadic
simple singularities of tangential family germs (in addition to two stable
singularities). We give their normal forms and miniversal tangential
deformations (i.e., deformations among tangential families), and we describe
the corresponding envelope perestroikas of small codimension. We also discuss
envelope singularities of non simple tangential families.
