Inclusion Criteria:

          -  Patients with evidence of relapsed or refractory AML or MDS following allogeneic stem
             cell transplantation

          -  Patients must have received preparative regimens to include either busulfan- or
             melphalan-based regimens

          -  Patient must have achieved myeloid engraftment as defined by an absolute neutrophil
             count >= 500 micro/L on 3 consecutive days

          -  Eastern Cooperative Oncology Group (ECOG) performance status =< 2

          -  Total bilirubin =< 2 times upper limit of normal (x ULN) (=< 3 x ULN if considered to
             be due to Gilbert's syndrome)

          -  Aspartate aminotransferase or alanine aminotransferase =< 2.5 x ULN

          -  Serum creatinine =< 2 x ULN or glomerular filtration rate (GFR) >= 50

          -  Patients must provide written informed consent

          -  The interval from the infusion of stem cells to time of initiation of nivolumab or
             ipilimumab will be at least 6 weeks (42 days)

          -  Females must be surgically or biologically sterile or postmenopausal (amenorrheic for
             at least 12 months) or if of childbearing potential, must have a negative serum or
             urine pregnancy test within 72 hours before the start of the treatment

          -  Women of childbearing potential must agree to use an adequate method of contraception
             during the study and until 3 months after the last treatment. Males must be surgically
             or biologically sterile or agree to use an adequate method of contraception during the
             study until 3 months after the last treatment

        Exclusion Criteria:

          -  Patients with known allergy or hypersensitivity to nivolumab or ipilimumab or any of
             their components

          -  Patients with acute GVHD > grade 2 at any time during the post-transplant course

          -  Patients with a known history of severe interstitial lung disease or severe
             pneumonitis or active pneumonitis that is uncontrolled in the opinion of the treating
             physician

          -  Patients with a known history of any of the following autoimmune diseases are
             excluded:

               -  Patients with a history of inflammatory bowel disease (including Crohn's disease
                  and ulcerative colitis)

               -  Patients with a history of rheumatoid arthritis, systemic progressive sclerosis
                  (scleroderma), systemic lupus erythematosus, autoimmune vasculitis (e.g.,
                  Wegener's granulomatosis)

          -  Patients with solid organ allografts (such as renal transplant) are excluded

          -  Ongoing immunosuppressive therapy for the treatment of GVHD. Patients receiving GVHD
             prophylaxis will be allowed on this study

          -  Patients with symptomatic central nervous system (CNS) leukemia at the time of
             evaluation or patients with poorly controlled CNS leukemia

          -  Active and uncontrolled disease/(active uncontrolled infection, uncontrolled
             hypertension despite adequate medical therapy, active and uncontrolled congestive
             heart failure New York Heart Association [NYHA] class III/IV, clinically significant
             and uncontrolled arrhythmia) as judged by the treating physician

          -  Patients with known human immunodeficiency virus seropositivity will be excluded

          -  Known to be positive for hepatitis B by surface antigen expression. Known to have
             active hepatitis C infection (positive by polymerase chain reaction or on antiviral
             therapy for hepatitis C within the last 6 months)

          -  Any other medical, psychological, or social condition that may interfere with study
             participation or compliance, or compromise patient safety in the opinion of the
             investigator

          -  Patients unwilling or unable to comply with the protocol

          -  Pregnant or breastfeeding