  In this paper we introduce a generalization of palindromic continued
fractions as studied by Adamczewski and Bugeaud. We refer to these generalized
palindromes as $m$-palindromes, where $m$ ranges over the positive integers. We
provide a simple transcendence criterion for $m$-palindromes, extending and
slightly refining an analogous result of Adamczewski and Bugeaud. We also
provide methods for constructing examples of $m$-palindromes. Such examples
allow us to illustrate our transcendence criterion and to explore the
relationship between $m$-palindromes and stammering continued fractions,
another concept introduced by Adamczewski and Bugeaud.
