Inclusion Criteria:

- Patients must have pathological confirmation (histologically or cytologically) of
relapsed or refractory acute myeloid leukemia (other than acute promyelocytic
leukemia), acute lymphocytic leukemia, or chronic myeloid leukemia in blast crisis

- The morphologic diagnosis of AML (non-APL), ALL, and CML in blast crisis will be made
independently by members of the hematologic pathology division; routine staining and
standard criteria as outlined by the Report of the NCI-Sponsored Workshop will be
followed

- All patients must have been refractory to or relapsed from their most recent therapy
AND are considered ineligible for potential curative approaches including allogeneic
stem cell transplant; in addition, patients must be at least:

- 3 weeks from last cytotoxic chemotherapy (excluding hydroxyurea)

- Hydroxyurea may be used for blast count control but must be discontinued within
48 hours of the initiation of BAY 43-9006

- 2 weeks from last radiation therapy

- 3 week from last biologic therapy (including myeloid growth factors)

- ECOG performance status =< 2 (Karnofsky >= 60%)

- Life expectancy of greater than 2 months

- Multilineage bone marrow failure due to the subject's underlying leukemia

- Total blast count in the peripheral blood < 30,000

- Total bilirubin =< 2 mg/dl

- AST(SGOT)/ALT(SGPT) =< 5 X institutional upper limit of normal

- Serum creatinine within normal institutional limits OR creatinine clearance >= 60
mL/min/1.73 m^2 for patients with creatinine levels above institutional normal

- All women of child-bearing potential and men must agree to use adequate contraception
(hormonal or barrier method of birth control; abstinence) prior to study entry and
for the duration of study participation; the effects of BAY 43-9006 on the developing
human fetus at the recommended therapeutic dose are unknown; however, kinase
inhibitors are known to be teratogenic; should a woman become pregnant or suspect she
is pregnant while participating in this study, she should inform her treating
physician immediately

- Ability to understand and the willingness to sign a written informed consent document

Exclusion Criteria:

- Patients with APL are not eligible for this clinical trial

- Patients who have not recovered from adverse events due to agents administered more
than 3 weeks earlier

- Patients with rapidly increasing peripheral blood blast counts (increase in the
absolute peripheral blast count > 50% within one week) or uncontrolled (absolute
blast count > 30,000) while on hydroxyurea will be excluded

- Patients with uncontrolled hypertension (i.e., persistent grade 3 while undergoing
treatment)

- Patients may not be actively receiving any other investigational agents

- Patients active and / or untreated CNS leukemia will not be eligible

- History of allergic reactions attributed to compounds of similar chemical or biologic
composition to BAY 43-9006

- Pregnant women are excluded from this study; breastfeeding should be discontinued if
the mother is treated with BAY 43-9006

- Patients with immune deficiency are at increased risk of lethal infections when
treated with marrow suppressive therapy; therefore, HIV-positive patients receiving
combination anti-retroviral therapy are excluded from the study because of possible
pharmacokinetic interactions with BAY 43-9006; appropriate studies will be undertaken
in patients receiving combination anti-retroviral therapy when indicated

- Uncontrolled intercurrent illness including, but not limited to, ongoing or active
infection, symptomatic congestive heart failure, unstable angina pectoris, cardiac
arrhythmia, or psychiatric illness/social situations that would limit compliance with
study requirements

- Patients must not have any evidence of bleeding diathesis

- Patients must not be on therapeutic anticoagulation; prophylactic anticoagulation
(i.e. low dose warfarin) of venous or arterial access devices is allowed provided
that the requirements for PT, INR or PTT are met

- Patients must not be taking the cytochrome P450 enzyme-inducing antiepileptic drugs
(phenytoin, carbamazepine, or phenobarbital), rifampin or St. John's wort