A Study of LY2603618 in Combination With Gemcitabine in Participants With Solid Tumors

Inclusion Criteria:

* Have histological or cytological or imaging evidence of a diagnosis of cancer that is advanced and/or metastatic disease
* Participant who is planned to have gemcitabine therapy at the proposed doses because he/she was not able to benefit from standard therapy and/or therapies known to provide clinical benefit or there is no standard therapy for the advanced and/or metastatic disease globally
* Have given written informed consent prior to any study-specific procedures
* Have adequate hematologic, hepatic and renal function
* Have a performance status of 0-2 on the Eastern Cooperative Oncology Group (ECOG) scale
* Have discontinued all previous therapies for cancer, including chemotherapy, cancer-related hormonal therapy, or other investigational therapy for at least 30 days (42 days for mitomycin C or nitrosoureas) prior to study enrollment and recovered from the acute effects of therapy
* Prior radiation therapy for treatment of cancer is allowed to less than 25% of the bone marrow, and participants must have recovered from the acute toxic effects of their treatment prior to study enrollment. Prior radiation to the whole pelvis is not allowed. Prior radiotherapy must be completed at least 30 days prior to study enrollment
* Males and females with reproductive potential must agree to use medically approved contraceptive precautions during the study and for 3 months after the last infusion of study drug
* Females with child bearing potential (not surgically sterilized and between menarche and 1 year post menopause) must have had a negative urine pregnancy test less than 7 days prior to the enrollment
* Are reliable and willing to make themselves available for the duration of the study and are willing to follow study procedures
* Have an estimated life expectancy of at least 12 weeks

Exclusion Criteria:

* Are currently enrolled in, or discontinued within the last 30 days from, a clinical study involving an off-label use of an investigational drug or device (other than the study drug used in this study), or concurrently enrolled in any other type of medical research judged not to be scientifically or medically compatible with this study
* Have serious preexisting medical conditions or serious concomitant systemic disorders that would compromise the safety of the participant or his/her ability to complete the study
* Have interstitial pneumonitis or pulmonary fibrosis, or previous history of them
* Have symptomatic central nervous system malignancy or metastasis
* Have current active infection
* Females who are pregnant or lactating
* Have known positive test results in human immunodeficiency virus (HIV), hepatitis B surface antigen (HBSAg), or hepatitis C antibodies (HCAb)
* Participants with acute or chronic leukemia or with any other disease likely to have a significant bone marrow infiltration
* Have previously completed or withdrawn from this study or any other study investigating LY2603618 or any other checkpoint kinase (Chk1) inhibitor
* Have known allergy to gemcitabine or LY2603618 or any ingredient of gemcitabine or LY2603618 (like Captisol®)
* Have an abnormal electrocardiogram (ECG) result that would put the participant at unnecessary risk in the opinion of the investigator