Air-writing refers to writing of characters or words in the free space by hand or finger movements. We address air-writing recognition problems in two companion papers. Part 2 addresses detecting and recognizing air-writing activities that are embedded in a continuous motion trajectory without delimitation. Detection of intended writing activities among superfluous finger movements unrelated to letters or words presents a challenge that needs to be treated separately from the traditional problem of pattern recognition. We first present a dataset that contains a mixture of writing and nonwriting finger motions in each recording. The LEAP from Leap Motion is used for marker-free and glove-free finger tracking. We propose a window-based approach that automatically detects and extracts the air-writing event in a continuous stream of motion data, containing stray finger movements unrelated to writing. Consecutive writing events are converted into a writing segment. The recognition performance is further evaluated based on the detected writing segment. Our main contribution is to build an air-writing system encompassing both detection and recognition stages and to give insights into how the detected writing segments affect the recognition result. With leave-one-out cross validation, the proposed system achieves an overall segment error rate of 1.15% for word-based recognition and 9.84% for letter-based recognition.