Functionalized ethylene-based polymers are prepared by a process comprising the step of reacting a first composition comprising an ethylene-based polymer with at least the following: (A) at least one carbon-carbon (C—C) free radical initiator of Structure I: wherein R1, R2, R3, R4, R5 and R6 are each, independently, hydrogen or a hydrocarbyl group; and wherein, optionally, two or more R groups (R1, R2, R3, R4, R5 and R6) form a ring structure; and with the provisos that (i) at least one of R2 and R5 is a hydrocarbyl group of at least two carbon atoms, and (ii) at least one of R3 and R6 is a hydrocarbyl group of at least two carbon atoms; and (B) at least one free radical initiator other than the carbon-carbon (C—C) free radical initiator of Structure I (a non-C—C free radical initiator), e.g., a peroxide; and (C) at least one functionalization agent, e.g., maleic anhydride.