We investigate the origin of the galaxy color-concentration bimodality at the bright-end of the luminosity function ( M _ { B } -5 \log h _ { 70 } < -18 mag ) with regard to the bulge-disc nature of galaxies . Via ( 2D ) surface brightness profile modeling with GIM2D , we subdivide the local galaxy population in the Millennium Galaxy Catalogue into one-component and two-component systems . We reveal that one-component ( elliptical and disc-only ) systems define the two peaks of the galaxy color-concentration distribution ( with total stellar mass densities of 0.7 \pm 0.1 and 1.3 \pm 0.1 \times 10 ^ { 8 } h _ { 70 } M _ { \odot } Mpc ^ { -3 } respectively ) , while two-component systems contribute to both a bridging population and the red , concentrated peak ( with total stellar mass densities of 1.1 \pm 0.1 and 1.8 \pm 0.2 \times 10 ^ { 8 } h _ { 70 } M _ { \odot } Mpc ^ { -3 } respectively ) . Moreover , luminous , ‘ bulge-less , red discs ’ and ‘ disc-less , blue bulges ’ ( blue ellipticals ) are exceptionally rare ( with volume -densities of 1.7 \pm 0.3 and 1.1 \pm 0.1 \times 10 ^ { -4 } h ^ { 3 } _ { 70 } Mpc ^ { -3 } respectively ) . Finally , within the two-component population we confirm a previously-reported correlation between bulge and disc color ( with a mean offset of only \left < ( u - r ) _ { \mathrm { bulge } } - ( u - r ) _ { \mathrm { disc } } \right > = 0.22 \pm 0.02 mag ) .