A hidden Markov model (HMM) based continuous speech recognition system is applied to on-line cursive handwriting recognition. The base system is unmodified except for using handwriting feature vectors instead of speech. Due to inherent properties of HMMs, segmentation of the handwritten script sentences is unnecessary. A 1.1% word error rate is achieved for a 3050 word lexicon, 52 character, writer-dependent task and 3%-5% word error rates are obtained for six different writers in a 25,595 word lexicon, 86 character, writer-dependent task. Similarities and differences between the continuous speech and on-line cursive handwriting recognition tasks are explored; the handwriting database collected over the past year is described; and specific implementation details of the handwriting system are discussed.