• To estimate the Treatment Success Rate of reaching a target of ≥ to 2x10^6 CD34+ cells/kg within 2 days of apheresis in Non-Hodgkin's Lymphoma (NHL), Hodgkin's Disease (HD) or Multiple Myeloma (MM) patients who are proven poor mobilizer [ Time Frame: 12 months ] [ Designated as safety issue: No ]
  

• To examine and compare the safety of both mobilization regimens, G-CSF plus AMD3100(240µg/kg) and G-CSF plus placebo in NHL, MM and HD patients [ Time Frame: After each dose of AMD3100 ] [ Designated as safety issue: Yes ]
  
• To measure the daily and total number of CD34+ cells harvested during apheresis. [ Time Frame: After each dose of AMD3100 ] [ Designated as safety issue: No ]
  
• To measure the number of days of apheresis needed to harvest greater than 2x10^6 CD34+ cells/kg [ Time Frame: After each dose of AMD3100 ] [ Designated as safety issue: No ]
  

This is a multicenter, randomized, comparative, patient-blinded study. Patients with NHL, HD or MM who would benefit from an autologous stem cell transplant, who failed previous collections or collection attempts with a mobilization regimen of chemotherapy with or wihoutG-CSF, and who meet the inclusion/exclusion criteria are eligible to receive AMD3100(240µg/kg) or placebo (both given as an evening dose).

Patients will undergo mobilization with G-CSF (10µg/kg) for 4 consecutive days. On Day 4, AMD3100 (240µg/kg) or placebo will be administered in the evening prior to the first apheresis and each subsequent evening prior to apheresis thereafter, such that there is a 10 to 11 hour interval between dosing and the initiation of apheresis. Patients will continue to receive G-CSF on each day of apheresis. G-CSF will be administered in the morning and approximately 1 hour prior to apheresis. Patients will undergo a minimum of 2 and a maximum of 7 aphereses until a minimum of 2x10^6 CD34+ cells/kg or greater than or equal to 5x10^6 CD34+cells/kg are collected. More cells may be collected, if done within the 7 aphereses. Patients who are to receive a tandem transplant will undergo a minimum of 2 and maximum of 7 aphereses until a minimum of 4x10^6 CD34+ cells/kg are collected. Aphereses should be performed on consecutive days (including weekend days)

The patient will have a peripheral blood (PB) sample collected to measure the number of CD34+ cell in PB at baseline prior to administration of G-CSF, prior to each administration of AMD3100 or placebo and at the initiation of apheresis. In addition, a sample will be obtained from each apheresis product to measure the number of CD34+ cells collected in the apheresis product.

Patients who fail to collect greater than or equal to 0.8x10^6 CD34+ cells/kg in 7 aphereses will be offered a rescue arm giving AMD3100 plus G-CSF.

Patients will undergo their ablative chemotherapy before transplantation. Patients will then be transplanted. The success of the transplantation will be evaluated. Graft durability will be evaluated to 12 months post-transplant. In the event that a sufficient number of cells for transplantation are not obtained from the collections, cells may be retained, pooled, and transplanted at a later date at the Investigator's discretion.