In this chapter, we study the metric properties of differential modules over nonarchimedean differential rings. The principal invariant that we identify is a familiar quantity from functional analysis, the spectral radius of a bounded endomorphism. When the endomorphism is the derivation acting on a differen- tial module, the spectral radius can be related to the least slope of the Newton polygon of the corresponding twisted polynomial. We give meaning to the other slopes as well by proving that over a complete nonarchimedean differential field, any differential module decomposes into components whose spectral radii are computed by the various slopes of the Newton polygon. However, this theorem will provide somewhat incomplete results when we apply it to p-adic differential modules in Part III; we will have to remedy the situation using Frobenius descendants and antecedents.