Results of first-principles band-structure calculations for theternary alkaline-earth silicon nitrides M2Si5N8 (M = Ca and Sr) are presented. In the structures ofM2Si5N8 (M = Ca, Sr and Ba), the N atoms showconnections to two (N[2]) and three (N[3]) neighbouringsilicon tetrahedral centres. Calculations show that the localelectronic structure is strongly dependent on the local chemicalbonding. The valence band is dominated by N 2p hybridized with thes, p states of the alkaline-earth-metal and silicon atoms. The upper partof the valence band is dominated by the 2p states of N[2]atoms, while the N[3] 2p states lie about 2 eV below the Fermilevel. The bottom of the conduction band consists of the N 3scharacters hybridized with s orbitals of the alkaline-earth metals,while the s character of Si atoms is higher in energy.Sr2Si5N8 is a semiconductor with a direct energy gapat Γ, while Ca2Si5N8 is an indirectsemiconductor. Optical diffuse reflectance spectra show an energygap of 4.9 eV for Ca2Si5N8, 4.5 eV forSr2Si5N8, as well as 4.1 eV forBa2Si5N8, in fair agreement with the calculatedvalues.