Keyword spotting refers to the process of retrieving all instances of a given keyword from a document. In the present paper, a novel keyword spotting method for handwritten documents is described. It is derived from a neural network-based system for unconstrained handwriting recognition. As such it performs template-free spotting, i.e., it is not necessary for a keyword to appear in the training set. The keyword spotting is done using a modification of the CTC Token Passing algorithm in conjunction with a recurrent neural network. We demonstrate that the proposed systems outperform not only a classical dynamic time warping-based approach but also a modern keyword spotting system, based on hidden Markov models. Furthermore, we analyze the performance of the underlying neural networks when using them in a recognition task followed by keyword spotting on the produced transcription. We point out the advantages of keyword spotting when compared to classic text line recognition.