Let (M) be the bounded continuous functions on a topological space M. "Almost linear" operators (and functionals) on C(M) are defined. Almost linearity does not imply linearity in general. However, it is shown that if M = [O, l] then any almost linear operator (or functional) must be linear. Specifically, if (a)0 implies T(f) 0, (b) T(f + g) = T(f) + T(g) whenever fg = 0, (c) T(f + g) = T(f) + T(g) whenever g is constant, and M[O, l], then T is linear. An application is given to convergence of measur.