A Study to Find Out How Safe and Effective Gammaplex® is in Young People With Primary Immunodeficiency

Inclusion Criteria: * The subject is between the ages of or is equal to 2 and 16 years of age, of either sex, belonging to any ethnic group, and above a minimum weight of 10 kg. This weight is based on the amount of blood required for testing. * The subject has a primary immunodeficiency disease, which has as a significant component of hypogammaglobulinemia and/or antibody deficiency (e.g. common variable immunodeficiency, X-linked and autosomal forms of agammaglobulinemia, hyper-IgM syndrome, Wiskott-Aldrich Syndrome). NB Isolated deficiency of a single IgG subclass, or of specific antibodies without hypogammaglobulinemia per se, does not qualify for inclusion. * Subjects already receiving IGIV replacement therapy require the following before their first infusion of Gammaplex: * Documented IGIV dose(s) and treatment intervals for the last 2 consecutive routine IGIV treatments (one of which can be the screening visit result). The previous doses should also meet the following conditions before study entry: Have not changed by ± 50% of the mean dose for at least 3 months; be between 300 and 800 mg/kg/infusion; be given every 21-28 days, inclusive; be a licensed or investigational product (Phase III or IIIb). * Documented previous IgG trough levels for the last 2 consecutive routine IGIV treatments for the last 2 consecutive routine IGIV treatments: Maintained at least 300 mg/dL above baseline serum IgG levels (defined as before initiation of any gamma globulin treatment for that subject); must be more than/equal to 600 mg/dL. * If a subject is a female of child-bearing potential, she must have a negative result on an HCG-based pregnancy test. * If a subject is a female who is or becomes sexually active, she must practice contraception by using a method of proven reliability for the duration of the study. * The subject is willing to comply with all aspects of the protocol, including blood sampling, for the duration of the study. * The subject, if old enough (generally 6 years to 16), has signed a Child Assent Form and the subject's parent or legal guardian has signed the Informed Consent Form, both approved by the IEC/IRB. Exclusion Criteria: * Has not been treated with IGIV (treatment naive subject) * The subject has a history of any severe anaphylactic reaction to blood or any blood-derived product. * The subject is known to be intolerant to any component of Gammaplex, such as sorbitol (i.e. intolerance to fructose). * The subject has selective IgA deficiency, history of reaction to products containing IgA, or has a history of antibodies to IgA. * Subjects who have completed the study and subjects who have withdrawn cannot participate in the study for a second time. * The subject is currently receiving, or has received, any investigational agent, other than an immune serum globulin (ISG) preparation that is being evaluated in a Phase III or IIIb study, within the prior 3 months. * The subject has been exposed to blood or any blood product or derivative within the last 6 months, other than a commercially available IGIV or other forms of commercially available and licensed ISG. If an unlicensed ISG product that is in Phase III or IIIb has been given, the subject cannot be infused with Gammaplex until 20 days after the last dose was given. * The subject is pregnant or is nursing. * The subject, at screening, has levels greater than 2.5 times the upper limit of normal as defined at the central laboratory of any of the following: (Alanine transaminase (ALT); Aspartate transaminase (AST) Lactate dehydrogenase (LDH)). * The subject has a severe renal impairment (defined as serum creatinine greater than 2 times the upper limit of normal or BUN greater than 2.5 times the upper limit of normal for the range of the laboratory doing the analysis); the subject is on dialysis; the subject has a history of acute renal failure. * The subject is known to abuse alcohol, opiates, psychotropic agents, or other chemicals or drugs, or has done so within the past 12 months. * The subject has a history of DVT, or thrombotic complications of IGIV therapy. * The subject suffers from any acute or chronic medical condition (e.g. renal disease or predisposing conditions for renal disease, or protein losing state) that, in the opinion of the investigator, may interfere with the conduct of the study. * The subject has an acquired medical condition, such as, chronic or recurrent neutropenia (ANC \< 1000 x 109/L) or AIDS known to cause secondary immune deficiency, or is post or recovering from hematopoietic stem cell transplantation. * The subject is receiving the following medication: Systemic long-term corticosteroids (i.e. not intermittent or burst, daily, \>1 mg of prednisone equivalent/kg/day). * The subject is receiving Immunosuppressive or Immunomodulatory drugs. * The subject has non-controlled arterial hypertension. * The subject has anemia (hemoglobin \<10 g/dL) at screening.