All alphanumeric characters can be written in certain styles with strokes of different shapes and positions. An on-line handwritten character written on a digitizing tablet is represented as a sequence of strokes, which are the loci of the pen tip from its pen-down to pen-up positions. In this paper, we present an approach to on-line handwritten alphanumeric character recognition based on sequential handwriting signals. In our approach, an on-line handwritten character is characterized by a sequence of dominant points in strokes and a sequence of writing directions between consecutive dominant points. The directional information of the dominant points is used for character pre-classification and the positional information is used for fine classification. Both pre-classification and fine classification are based on dynamic programming matching using the idea of band-limited time warping. These techniques are elastic, in that they can tolerate local variation and deformation. The issue of reference (or template) set evolution is also addressed. A recognition experiment has been conducted with 62 character classes (0-9, A-Z, a-z) of different writing styles (Italian manuscript style and some other styles) and 21 people as data contributors. The recognition rate of this experiment is 91%, with 7.9% substitution rate and 1.1% rejection rate. The average processing time is 0.35 s per character on a 486 50 MHz personal computer.