This paper investigates the characterizations of threshold/ramp schemes which give rise to time-dependent threshold schemes. These schemes are called "dynamic threshold schemes" as compared to the conventional time-independent threshold cheme. In a (d, m, n, T) dynamic threshold scheme, there are n secret shadows and a public shadow, pj, at time t=tj 1≦tj≦T. After determining any m shadows, m≦n, and the public shadow, pj, we can easily recover d master keys, Kj1,Kj2,..., and Kjd. Furthermore, if the d master keys have to be changed to K1j-1,K2j-1,..., and Kdj-1 for some security reasons, only the public shadow, pj, has to be changed to pj+1. All the n secret shadows issued initially remain unchanged. Compared to the conventional threshold/ramp schemes, at least one of the previously issued n shadows needs to be changed whenever the master keys need to be updated for security reasons. A (1, m, n, T) dynamic threshold scheme based on the definition of cross-product in an N-dimensional linear space is proposed to illustrate the characterizations of the dynamic threshold schemes.