This paper investigates the structure and degeneracy in the table of quadratic Hennite-Padé forms. In §2 it is noted that a space of quadratic Hennite-Padé forms for f(x) may be multidimensional and the optimal choice of a representative form is discussed. In §3 the structure of the table of quadratic Hennite-Padé forms is considered. The Padé case is considered first and it is suggested that a D-table of degenerate Padé forms is perhaps a better indication of the structure than the more traditional C-table. The usual table of Padé approximants may be deduced from the D-table in much the same way as it is from the C-table. An analagous structure is deduced for the D-table of quadratic Hermite-Padé forms. This idea can be applied to general Hermite-Padé forms.