A Safety, Tolerability, and Immunogenicity Study of mRNA-1345 and mRNA-1365 in Participants Aged 5 Months to <24 Months

Inclusion Criteria: * The participant is 8 months to \<24 months (Part A), 5 months to \<8 months (Part B), or 8 months to \<12 months (Part C) of age at the time of randomization (Day 1/Baseline visit), who is in good general health, in the opinion of the Investigator, based on review of medical history and screening physical examination. * In the Investigator's opinion, the parent(s)/ legally authorized representative (LAR)(s) understand and are willing and physically able to comply with protocol-mandated follow up, including all procedures, and provide written informed consent. * The participant is growing normally for age in the opinion of the site clinician in the months prior to enrollment. * The participant was born at full-term (≥37 weeks gestation) with a minimum birth weight of 2.5 kilograms (kg). * For Part C Cohort 7: participant must have received nirsevimab ≥6 months prior to Day 1 Visit. * For Part C Cohort 8: participant was eligible at any time since birth, according to national guidelines, to receive nirsevimab prior to Day 1 Visit but did not do so. Exclusion Criteria: * Has a known history of symptomatic RSV (Part A: within 3 months; Part B and Part C: since birth) or hMPV infection (Part A: within 3 months; Part B: since birth) prior to administration of the first dose of investigational product (IP) or has a known close contact with anyone with laboratory-confirmed RSV (Parts A, B, and C) or hMPV infection (Parts A or B) within 14 days prior to administration of the first dose of IP. * Is acutely ill or febrile 24 hours prior to or at the screening visit. Fever is defined as a body temperature ≥38.0°Celsius/≥100.4°Fahrenheit. Participants who meet this criterion may have visits rescheduled within the relevant study visit windows. * Has previously been administered an investigational or approved vaccine for prevention of RSV (Parts A, B, and C) or hMPV (Parts A and B) infection or if the participant's mother received an investigational or approved vaccine for the prevention of RSV (Parts A, B, and C) or hMPV (Parts A and B) infection during pregnancy. * Has received investigational or approved agents for prophylaxis against RSV or hMPV (for example, monoclonal antibodies) or is intending to receive these during the course of the study. For Part C (Cohort 7 only), use of nirsevimab ≥6 months before Day 1 Visit is allowed. * Has a known hypersensitivity to a component of the vaccine or its excipients. Hypersensitivity includes, but is not limited to, anaphylaxis or immediate allergic reaction of any severity to a previous dose of an mRNA vaccine or any of its components (including polyethylene glycol or immediate allergic reaction of any severity to polysorbate). * Has a medical condition that, according to the Investigator's judgment, may pose additional risk as a result of participation, interfere with safety assessments, or interfere with interpretation of results. Note: Other protocol-defined inclusion/exclusion criteria apply.