A new form of source coding subject to a fidelity criterion, called sliding-block coding, has recently been introduced by Gray, Neuhoff, and Ornstein. A method of conversion from block coding to sliding-block coding, or vice versa, with an arbitrarily small increase in rate is shown for ergodic sources. The ergodic theorem is used to convert from sliding-block codes to block codes. A theorem similar to one of Rohlin is used to convert from block codes to sliding-block codes. A proof of this theorem and some discussion of the nonergodic case appear in the appendices.