  In this article we study the notion of supermanifolds families, starting from
Green's general classification of supermanifolds. The topics studied divide
this article into two distinct parts, labelled I and II respectively. Part I
concerns the splitting type of a supermanifold and our attempt to construct
variations thereof. In Part II we look at a particular class of families,
referred to as `$gtm$-families'. We are concerned with the notion of a
`secondary obstruction theory', which is apparent in any $gtm$-family of
supermanifolds over a (connected and Stein) non-reduced, superspace base.
