Single- and double-wall carbon nanotubes (CNTs) having dimethylanilino (DMA) units covalently attached to the external graphene wall have been prepared by the reaction of the dimethylaminophenylnitronium ion with the corresponding CNT. The samples have been characterized by Raman and XPS spectroscopies, thermogravimetry, and high-resolution transmission electron microscopy in which the integrity of the single or double wall of the CNT and the percentage of substitution (one dimethylanilino group every 45 carbons of the wall for the single- and double-wall samples) has been determined. Nanosecond laser flash photolysis has shown the generation of transients that has been derived from the charge transfer between the dimethylanilino (as the electron donor) to the CNT graphene wall (as the electron acceptor). Importantly, the lifetime of the double-wall CNT is much shorter than that monitored for the single-wall CNT. Shorter-lived transients were also observed for the pentyl-esterified functionalized double-wall CNT with respect to the single-wall analogue in the presence of hole (CH3OH) and electron quenchers (O2, N2O), which has led to the conclusion that the inner, intact graphene wall that is present in double-wall CNT increases the charge mobility significantly, favoring charge recombination processes. Considering the importance that charge mobility has in microelectronics, our finding suggests that double-wall CNT or two-layer graphene may be more appropriate to develop devices needing fast charge mobility.