We study the normality of families of meromorphic functions defined in terms of certain omitted functions. In particular, we prove the following results. Firstly, if is a family of meromorphic functions in a domain D ⊂ ℂ, and a(z), b(z) and c(z) are distinct meromorphic functions in D and if, for all f ∈ and all z ∈ D, f(z) ≠ a(z), f(z) ≠ b(z) and f(z) ≠ c(z), then is normal in D. Secondly, letting R(w) be a rational function of degree greater than or equal to 3 and be a family of functions meromorphic in a domain D ⊂ ℂ, if there exists a non-constant meromorphic function α(z) in D such that, for all f ∈ and z ∈ D, R(f(z)) ≠ α(z), then is normal in D.