Recently, a novel swine-origin influenza A/H1N1 virus was identified as a significant cause of febrile respiratory illnesses in Mexico and the United States. It rapidly spread to many countries around the world, prompting the World Health Organization (WHO) to declare a pandemic on June 11, 2009. Data from several cohorts in different age groups that received licensed trivalent seasonal influenza vaccines suggest that these vaccines are unlikely to provide protection against the new virus. In addition, adults are more likely to have measurable levels of serum hemagglutination inhibition assay (HAI) or neutralizing antibody than are children. These data indicate the need to develop vaccines against the new H1N1 strain and suggest that different vaccine strategies (e.g., number of doses, need for adjuvant) may be appropriate for persons in different age groups. If the novel influenza H1N1 2009 virus continues to circulate, it is possible that it will co-circulate with the non-pandemic seasonal influenza strains. In this situation, it might be beneficial to co-administer an H1N1 vaccine concurrent with the seasonal inactivated influenza vaccine. This protocol will explore if vaccination with the 2009-2010 licensed seasonal trivalent influenza vaccine (TIV) has an effect on antibody response to the novel influenza H1N1 2009 virus. This protocol will also examine if receiving the H1N1 vaccine either concurrent with, prior to, or following the seasonal influenza vaccine affects the antibody response to the seasonal influenza vaccine. A randomized Phase II study in infants, toddlers, children and adolescents. This study is designed to investigate the safety, reactogenicity, and immunogenicity of an inactivated influenza H1N1 virus vaccine when given concurrent with seasonal TIV, or sequentially with (before or after) seasonal influenza vaccine. Primary objectives are: safety, to assess the safety of the unadjuvanted, inactivated H1N1 vaccine when administered either concurrent with, prior to, or following licensed seasonal influenza vaccination; and immunogenicity, to assess the effect of TIV administration on antibody response to unadjuvanted, inactivated H1N1 vaccine as assessed by HAI, stratified by age of recipient. The secondary objective is: immunogenicity, to assess the effect of H1N1 vaccine administration on antibody response to TIV as assessed by HAI, stratified by age of recipient. Subjects will be randomized into 4 groups, stratified by age (150 subjects per group with 50 subjects per age stratum: greater than or equal to 6-<36 months, greater than or equal to 36 months-9 years, and 10-17 years), to receive two 15 mcg doses of inactivated influenza H1N1 vaccine at Days 0 and 21 followed by TIV on Day 42 (Group 1), two 15 mcg doses of H1N1 vaccine of which the first dose is administered concurrently with TIV (Group 2), two 15 mcg doses of H1N1 vaccine of which the second dose is administered concurrently with TIV (Group 3), or TIV administered on Day 0 followed by two 15 mcg doses of H1N1 vaccine on Days 21 and 42 (Group 4). Following immunization, safety will be measured by assessment of adverse events for 21 days following the last vaccination (Day 42 for those who do not receive the second dose), serious adverse events and new-onset chronic medical conditions for 8 months post first vaccination (Day 201 for Groups 2 and 3 or Day 222 for Groups 1 and 4), and reactogenicity to the vaccines for 8 days following each vaccination (Day 0-7). Immunogenicity testing will include HAI and neutralizing antibody testing prior to vaccination, on the day of each vaccination (Days 0, 21 and 42) and 21 days following the third vaccine.