This is an open-label (all people know the identity of the intervention), Phase 1 dose escalation, 2-part study (Part I and Part II). In Part I of the study, the Maximum Tolerated Dose (MTD) defined as the highest dose with an observed incidence of dose limiting toxicity (DLT) in no more than 1 in 6 patients, will be determined using rapid escalation (Stage 1) followed by conventional escalation (Stage 2). In Stage 1, at least 2 patients will be enrolled at each dose level; dose increments of 100% will be applied. In Stage 2, at least 3 patients will be enrolled at each dose level and dose increments of 20-50% will be implemented. Decisions on dose escalation or de-escalation, changes in the timing of pharmacokinetic/pharmacodynamic sampling, and the exploration of an alternative schedule were to be made by the Study Evaluation Team (SET), which consisted of all principal investigators, the medical monitor, and 1 of the sponsor's clinical pharmacologists. Part II of the study will be the expansion phase, which will begin after the MTD had been determined in Part I and an additional cohort of patients with MDS will be enrolled to further explore the safety and activity of JNJ 26481585 in patients with MDS. The starting dose for patients enrolled in Part II of the study was to be the MTD established in Part I. Depending on the outcome, the SET may decide to continue at the MTD dose, or dose-de-escalate to the next lower level (25 50% decrement from MTD). The cohort for MDS will be expanded to consist of 16 evaluable patients. Safety will be evaluated throughout the study and will include evaluations of adverse events clinical laboratory tests, electrocardiogram (ECG), vital signs, 24 hours Holter ECG, physical examination, Eastern Cooperative Oncology Group performance status and Multiple Gated Acquisition scan or echocardiography.