Let F be a meromorphic function in the complex plane. We investigate the behaviour of the iterates of F in a Baker domain B. In particular, we describe the dynamics of the orbits with the help of conformal conjugacies; that is, we determine a function φ which is univalent in a large simply connected subdomain of B such that φ(F(z))=T(φ(z)) holds throughout B. Here T is either a parabolic or hyperbolic Möbius transformation mapping either a half plane or [Copf ] onto itself. This functional equation is always solvable in a Baker domain if F has only finitely many poles. Moreover, there is an example of a function with infinitely many poles where one cannot find an appropriate conformal conjugacy in an invariant Baker domain.