In this chapter, we study p-adic differential modules in a situation left untreated by our preceding analysis, namely when the intrinsic generic radius of convergence is equal to 1 everywhere (the Robba condition). This setting is loosely analogous to the study of regular singularities of formal meromorphic differential modules considered in Chapter 7; in particular, there is a meaningful theory of p-adic exponents in this setting. However, some basic considerations indicate that p-adic exponents must necessarily be more complicated than the exponents considered in Chapter 7. For instance, the p-adic analogue of the Fuchs theorem can fail unless we impose a further condition: the difference between exponents must not be p-adic Liouville numbers. With this in mind, we may proceed to construct p-adic exponents for differential modules satisfying the Robba condition. Such modules carry an action of the group of p-power roots of unity via Taylor series; under favorable circumstances, the module splits into isotypical components for the characters of this group. We may identify these characters with elements of Z_??, and these give the exponents.