We have observed single photon double K-shell photoionization in the C(2)H(2n) (n=1-3) hydrocarbon sequence and in N(2) and CO, using synchrotron radiation and electron coincidence spectroscopy. Our previous observations of the K(-2) process in these molecules are extended by the observations of a single photon double photoionization with one core hole created at each of the two neighboring atoms in the molecule (K(-1)K(-1) process). In the C(2)H(2n) sequence, the spectroscopy of K(-1)K(-1) states is much more sensitive to the bond length than conventional electron spectroscopy for chemical analysis spectroscopy based on single K-shell ionization. The cross section variation for single photon K(-1)K(-1) double core ionization in the C(2)H(2n) sequence and in the isoelectronic C(2)H(2n), N(2) and CO molecules validates a knock-out mechanism in which a primary ionized 1s photoelectron ejects another 1s electron of the neighbor atom. The specific Auger decay from such states is clearly observed in the CO case.