Inclusion Criteria:

- Diagnosis of persistent or recurrent WHO classification diffuse large B-cell
lymphoma, composite lymphoma with > 50% diffuse large B-cell lymphoma, mediastinal
B-cell lymphoma, immunoblastic, plasmablastic, Burkitt's or Burkitt-like or classical
Hodgkin's lymphoma. Patients transformed from follicular lymphoma are eligible for
the study, pending fulfillment of other criteria.

- 15 years old or older

- Three or fewer prior regimens of chemotherapy over the entire course of their disease
treatment (including one induction chemotherapy and no more than 2 salvage
chemotherapies). Monoclonal antibody therapy and involved field radiation therapy
will not be counted as prior therapies.

- All patients must have chemosensitive disease as demonstrated by at least a partial
response to induction or salvage therapy.

- Less than or equal to 10% bone marrow involvement.

- Patients with adequate organ function as measured by: a)Cardiac: American Heart
Association Class I: Patients with cardiac disease but without resulting limitation
of physical activity. Ordinary physical activity does not cause undue fatigue,
palpitation, dyspnea, or anginal pain. Additionally, all patients must have a left
ventricular ejection fraction at rest greater than or equal to 40% demonstrated by
MUGA or echocardiogram; b)Hepatic: (i) Bilirubin less than 2.0 mg/dL (except for
isolated hyperbilirubinemia attributed to Gilbert syndrome or antiretroviral therapy)
and ALT and AST greater than 3x the upper limit of normal; (ii) Concomitant
Hepatitis: Patients with chronic hepatitis B or C may be enrolled on the trial
providing the above criteria are met. In addition, no active viral replication -
undetectable (viral load less than 500 copies/ml) hepatitis B DNA level by PCR and no
clinical or pathologic evidence of irreversible chronic liver disease; c)Renal:
Creatinine clearance (calculated creatinine clearance is permitted) greater than 40
mL/min; d)Pulmonary: DLCO, FEV1, FVC greater than or equal to 45% of predicted
(corrected for hemoglobin).

- Autologous peripheral stem cell graft with a minimum of greater than or less than 1.5
x 10^6 CD 34+ cells/kg (target greater than or less than 2.0 x 10^6 CD 34+ cells/kg)
or if PBSC mobilization fails, cells can be obtained by bone marrow harvest per
institutional practices (in cases where bone marrow will be used for transplantation,
the required CD34+ dose does not apply and institutional requirements for total
nucleated cell dose should apply).

- Initiate conditioning therapy within 3 months of mobilization or bone marrow harvest.

- Signed informed consent.

- Patients on antiretroviral therapies (ARVs) can either have: a) Undetectable HIV
viral load (VL less than 50 copies); b) If VL detectable at less than 2000 copies/mL
must have review of previous antiretroviral regimens or previous genotypic or
phenotypic testing which indicate the ability to fully suppress virus by addition of
sensitive drugs. This review will be carried out by the ID specialist caring for the
patient; c)If VL detectable at greater than 2000 copies/mL, a current HIV genotype
and/or phenotype must be obtained. If a HAART regimen to which the patient's virus
is sensitive can be determined based on genotype and previous antiretroviral
experience, then the patient will be considered eligible in this regard. This review
will be carried out by the ID specialist caring for the patient.

Exclusion Criteria:

- Karnofsky performance score less than 70%.

- Uncontrolled bacterial, viral or fungal infection (currently taking medication and
with progression or no clinical improvement).

- Prior malignancy in the 5 years prior to enrollment except resected basal cell
carcinoma, treated cervical carcinoma in situ or Kaposi's sarcoma: a)Symptomatic
Kaposi's sarcoma currently requiring therapy is excluded (patients receiving topical
therapy for minimal disease are not included in this definition); b)Prior treatment
with topical agents, local radiation, or up to 6 cycles of cytotoxic chemotherapy at
least six months prior is permitted; c) Other cancers treated with curative intent
less than 5 years previously will not be allowed unless approved by the Medical
Monitor or Protocol Chair; d)Cancer treated with curative intent more than 5 years
previously will be allowed.

- Pregnant (positive β-HCG) or breastfeeding.

- Fertile men or women unwilling to use contraceptive techniques from the time of
initiation of mobilization until six-months post-transplant.

- Prior autologous or allogeneic HCT.

- Patients with evidence of MDS/AML or abnormal cytogenetic analysis indicative of MDS
on the pre-transplant bone marrow examination. Pathology report documentation need
not be submitted.