Inclusion Criteria:

          1. Patients must have a diagnosis of one of the following:

               -  MDS (Arm A): High-risk MDS defined as: >5% blasts in bone marrow and/or the
                  following cytogenetic categories: presence of inv(3)/t(3q)/del(3q), -7/del(7q),
                  complex cytogenetics (3 or more abnormalities)

               -  AML (Arm B): Relapsed/refractory/unable to tolerate conventional chemotherapy

               -  MDS or AML as above BUT with prior therapy with Azacitibine (Arm C): Patients who
                  meet criteria for either Arm A or Arm B but have been treated or are currently
                  treated with Azacitibine *Note: As of July 2018, only high risk MDS patients will
                  be eligible as Arm B is closed. As of October 2017, those patients with MDS who
                  have received prior treatment will now be enrolled in Arm A as Arm C is closed.

          2. Patients must be ≥ 18 years old

          3. Patients must have an ECOG performance status of <= 2 (see Attachment 1).

          4. Patients must have a life expectancy of at least 4 weeks.

          5. Patients must be able to consume oral medication.

          6. Patients must have completed any radiotherapy four weeks prior to study entry, 0-2
             weeks for local palliative XRT (small port).

          7. Patients must have recovered from the toxic effects of any prior chemotherapy to <
             Grade 2 (except for alopecia).

          8. Required initial laboratory values: Creatinine≤ 2.0mg/dL; total or direct bilirubin ≤
             1.5mg/dL (if not due to the leukemia itself or known Gilbert's Syndrome);(as
             documented by treating physician) SGPT(ALT) ≤ 3xULN; glucose <200 mg/dL, negative
             pregnancy test for women of child-bearing potential.

          9. Patients must be able to sign consent and be willing and able to comply with scheduled
             visits, treatment plan and laboratory testing.

         10. Patients may have had a prior stem cell transplant (autologous or allogeneic), however
             they may not have active GvHD, nor be on any immunosuppression

        Exclusion Criteria:

          1. Patients must not be receiving any chemotherapy agents (except Hydroxyurea)

               -  Intrathecal ARA-C and intrathecal methotrexate are permissible (as they are not
                  systemic and only isolated to the central nervous system).

               -  Patients can not have received more than 3 prior lines of therapy for their
                  hematologic malignancy. Patient may have previously had azacitidine or decitabine
                  will be eligible to enroll on Arm A (MDS)

          2. Patients must not be receiving growth factors.

          3. Patients with a current second malignancy requiring systemic therapy, other than
             non-melanoma skin cancers, are not eligible. If a patient has had a prior second
             malignancy that is not currently requiring active treatment, the patient will be
             considered eligible.

          4. Patients with uncontrolled high blood pressure, unstable angina, symptomatic
             congestive heart failure, myocardial infarction within the past 6 months or serious
             uncontrolled cardiac arrhythmia are not eligible.

          5. Patients may not take any of the following medications while on study, but will be
             considered eligible if medication is discontinued 72 hrs prior to first dose of
             Sirolimus:

               -  Carbamazepine (e.g. Tegretol)

               -  Rifabutin (e.g. Mycobutin)

               -  Rifampin (e.g. Rifadin)

               -  Rifapentine (e.g. Priftin)

               -  St. John's Wort- may decrease effects of sirolimus by decreasing the amount of
                  sirolimus in the body

               -  Clarithromycin (e.g. Biaxin)

               -  Cyclosporin e.g. (Neoral or Sandimmune)

               -  Diltiazem (e.g. Cardizem)

               -  Erythromycin (e.g. Akne-Mycin, Ery-Tab)

               -  Itraconazole (e.g. Sporanox)

               -  Fluconazole (e.g. Diflucan)

               -  Ketoconazole (e.g. Nizoral)

               -  Telithromycin (e.g. Ketek)

               -  Verapamil (e.g. Calan SR, Isoptin, Verelan)

               -  Voriconazole (e.g. VFEND) - May increase the effects of sirolimus by increasing
                  the amount of this medicine in the body. Can take 72 hours after last dose of
                  Sirolimus

               -  Tacrolimus (e.g. Prograf) - May cause liver transplant rejection or serious side
                  effects in patients on sirolimus.

          6. Patients with known HIV positivity or AIDS-related illness are not eligible.

          7. Patients with other severe concurrent disease which in the judgment of the
             investigator would make the patient inappropriate for entry into this study are
             ineligible.

          8. Patients must not have received any investigational agents within 21days of study
             entry.

          9. Patients must not be pregnant or breastfeeding. Pregnancy tests must be obtained for
             all females of child-bearing potential. Pregnant or lactating patients are ineligible
             for this study due to the unknown human fetal or teratogenic toxicities of rapamycin.
             Males or females of reproductive age may not participate unless they have agreed to
             use an effective contraceptive method.

         10. Patients who have uncontrolled infection are not eligible. Patients must have any
             active infections under control. Fungal disease must be stable for at least 2 weeks
             before study entry. Patients with bacteremia must have documented negative blood
             cultures prior to study entry.