This is a study of dulaglutide in Chinese participants. The purpose of the study is to determine how the body processes dulaglutide and how dulaglutide affects the body. This study has 2 parts: Part A - single dose of dulaglutide administered to healthy participants in 2 of 3 study periods. There is a minimum 28-day washout between periods. Part A will last approximately 16 weeks. Part B - multiple doses of dulaglutide administered to participants with Type 2 diabetes mellitus (T2DM). Part B will last approximately 15 weeks.

Doses of 0.5 milligrams (mg), 0.75 mg, and 1.5 mg of dulaglutide will be evaluated in this study.

Inclusion Criteria:

All Participants:

• Native Chinese (all 4 grandparents of Chinese origin)
• Male participants with female partners of child-bearing potential, or partners who are pregnant or breastfeeding, agree to use a reliable method of contraception from the time of the first dose until 3 months after the last dose of investigational product, as determined by the investigator.
• The method of contraception may be one of the following: condom with spermicidal agent, male participant sterilization, true abstinence (which is in line with the participant's usual lifestyle choice; withdrawal or calendar methods are not considered acceptable).
• Female participants not of child-bearing potential (i.e. are postmenopausal or permanently sterilized [e.g. tubal occlusion, hysterectomy, bilateral salpingectomy]). Such participants will not be required to use contraception but must test negative for pregnancy at the time of enrollment. Postmenopausal is defined as at least 1 year post cessation of menses (without an alternative medical cause) or at least 1 year of spontaneous amenorrhea, with follicle stimulating hormone (FSH) ≥40 milli international units per milliliter (mIU/mL).
• Female participants who have undergone sterilization by tubal ligation: agree to use a condom in conjunction with spermicidal gel, foam, cream, film or suppository from the time of screening until 3 months after the last dose of investigational product. Such participants must also test negative for pregnancy at the time of enrollment.

Participants with T2DM:

• Have T2DM controlled with diet or exercise alone or with a single oral agent antihyperglycemic medication (OAM) (metformin, sulfonylureas, meglitinides, acarbose [or other disaccharidase inhibitors] or thiazolidinediones) for at least 3 weeks (3 months for thiazolidinediones) before admission. Note that participants receiving sulfonylureas, meglitinides or acarbose may participate only if this treatment is stopped and metformin substituted. If switched to metformin, participants should be allowed to stabilize on metformin for 3 weeks before receiving study drug.
• If T2DM controlled with diet or exercise alone, must have a hemoglobin A1c (HbA1c) value of 6.5% to 10.5% at screening and a fasting blood glucose value of 126 to 250 milligrams per deciliter (mg/dL) (approximately 7.0 to 13.9 millimoles per liter [mmol/L]) at screening.
• If T2DM controlled with OAM(s), must have an HbA1c value of 9.0% or less at screening and a fasting blood glucose value of 110 to 200 mg/dL (approximately 6.1 to 11.1 mmol/L) at screening. If a participant's T2DM is being controlled with OAM(s) other than metformin, the participant's OAM will be stopped for at least 3 weeks before administration of study drug.

Exclusion Criteria:

All Participants:

• Have a history or presence of cardiovascular (myocardial infarction, cerebrovascular accident, venous thromboembolism), respiratory, hepatic, renal, hematological, neurological autoimmune or endocrine (except T2DM), disorders capable of significantly altering the absorption, metabolism, or elimination of drugs; of constituting a risk when taking the study medication; or of interfering with the interpretation of data.
• Have evidence of significant active neuropsychiatric disease.
• Have poorly controlled hypertension (systolic >160 millimeters of mercury [mmHg] and/or diastolic >100 mmHg) and/or evidence of labile blood pressure including symptomatic postural hypotension.
• Have a history or presence of pancreatitis (history of chronic pancreatitis or idiopathic acute pancreatitis) or gastrointestinal disorder, for example relevant esophageal reflux or gall bladder disease, or any gastrointestinal disease which impacts gastric empty (for example, gastric bypass surgery, pyloric stenosis, with the exception of appendectomy) or could be aggravated by glucagon-like peptide-1 (GLP-1) analogs or dipeptidyl peptidase (DPP)-4 inhibitors. Participants with dyslipidemia, and participants who had cholecystolithiasis (removal of gall stones) and/or cholecystectomy (removal of gall bladder) in the past, with no further sequelae, may be included in the study at the discretion of the screening physician.
• Have personal or family history of medullary thyroid cancer (MTC) or a genetic condition that predisposes to MTC.

Participants with T2DM

• Have experienced outpatient use of insulin for control of diabetes within the past 6 months.
• Have clinically significant peripheral vascular occlusive disease in the opinion of the investigator.
• Have known severe exudative diabetic retinopathy in the opinion of the investigator.
• Have known significant autonomic neuropathy as evidenced by urinary retention, diabetic diarrhea, or gastroparesis.
• Have experienced a ketoacidotic episode (pH less than 7.3) requiring hospitalization in the last 6 months.
• Regular use of drugs that affect the glycodynamics and that directly reduce gastrointestinal motility (eg, anticholinergics, antispasmodics, 5HT3 antagonists, dopamine antagonists, and opiates) and of systemic corticosteroids by oral, intravenous, or intramuscular route, or potent, inhaled, or intranasal steroids known to have a high rate of systemic absorption.

All enrolled participants.