Inclusion Criteria:

          -  Subjects must be newly diagnosed or previously diagnosed with CNL or aCML; all
             patients must have a bone marrow biopsy completed during the screening or baseline
             period if one has not been done within 90 days of day 1, cycle one

          -  Subjects must have platelet count greater than 25,000 per microliter at baseline and
             at the start of study (day 1, cycle 1) visit

          -  Subjects must be able to discontinue any drug treatment aimed at lowering disease
             burden in CNL or aCML; subjects should discontinue hydroxyurea to treat underlying CNL
             or aCML disease no later than day -7 (one week before starting ruxolitinib); for drugs
             that have more long-lasting effects on the marrow, such as thalidomide and its
             analogs, and interferon, subjects should discontinue these no later than day -28

          -  Subjects must be willing to accept/continue transfusions to treat low hemoglobin
             levels

          -  Subjects must have a life expectancy of > 6 months

        Exclusion Criteria:

          -  Subjects unable to review and sign informed consent form

          -  Females who are pregnant or breastfeeding, and males and females who cannot comply
             with requirements to avoid fathering a child or becoming pregnant

          -  Subjects with known diagnosis of human immunodeficiency virus (HIV) or chronic active
             Hepatitis B or C; viral testing is not required; subjects with a history of Hepatitis
             B and/or C are allowed on trial if the virus is undetected at the time of enrollment

          -  Subjects with inadequate liver (alanine aminotransferase [ALT]/serum glutamate
             pyruvate transaminase [SGPT] above 4 X upper limit of normal [ULN] or direct bilirubin
             4 X ULN AND the lab abnormalities are felt to be due to underlying liver dysfunction)

          -  Subjects with end stage renal function (creatinine clearance [CrCl] < 15 mL/min or
             glomerular filtration rate [GFR] <15 mL/min) regardless of whether hemodialysis is
             required

          -  Subjects with clinically serious infections requiring ongoing antibiotic therapy

          -  Subjects with severe (immediately life threatening) and recent (occurring within the
             last 3 months) cardiac dysfunction, pulmonary dysfunction, esophageal variceal
             bleeding, hemorrhagic strokes, or intracranial hemorrhage are not eligible for study
             participation

          -  Subjects requiring therapeutic doses of anticoagulation or anti-platelet therapies
             (aspirin above 81 mg daily, Plavix or similar agents) AND platelet counts are below
             50,000 on two different laboratory evaluations, separated by minimum of two weeks

          -  Taking investigational or commercial agents or therapies with the intent to treat the
             subject's malignancy other than those therapies permitted

          -  Subjects with invasive malignancy over the previous 2 years except treated early stage
             carcinomas of the skin, completely resected intraepithelial carcinoma of the cervix,
             and completely resected papillary thyroid and follicular thyroid cancers

          -  Previous allergic reactions to janus kinase (JAK) inhibitors or excipients

          -  Prior therapy with ruxolitinib or other JAK inhibitors

          -  Subjects who have had major surgery within 4 weeks prior to entering the study

          -  Subjects who are anticipated to receive a transplant within the first 6 months of
             treatment on trial