We tackle the problem of detecting global variables in functional programs. We present syntactic criteria for single-threading which improves upon previous solutions (both syntactic and semantics-based) in that it applies to higher-order languages and to most sequential evaluation strategies. The main idea of our approach lies in the use of continuations. One advantage of continuation expressions is that evaluation ordering is made explicit in the syntax of expressions. So, syntactic detection of single-threading is simpler and more powerful on continuation expressions. We present the application of the analysis to the compilation of functional languages, semantics-directed compiler generation and globalization-directed transformations (i.e. transforming non-single-threaded expressions into single-threaded ones). Our results can also be turned to account to get single-threading criteria on regular λ-expressions for different sequential evaluation orders.