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dysgammaglobulinemia

n. An immune disorder characterized by a reduction in some (but not all) types of gamma globulins.

Wikipedia
Dysgammaglobulinemia

Dysgammaglobulinemia is a type of immune disorder characterized by a reduction in some types of gamma globulins.

It is distinguished from hypogammaglobulinemia, which is a reduction in all types of gamma globulins.

Hyper IgM syndrome can be considered a form of dysgammaglobulinemia, because it results from a failure of transformation from IgM production to production of other antibodies, and so the condition can be interpreted as a reduction of the other types.