We have determined the physical ground state properties of the compounds CeRuPO and CeOsPO by means of magnetic susceptibility chi(T), specific heat C(T), electrical resistivity rho(T), and thermopower S(T) measurements. chi(T) reveals a trivalent 4f1 cerium state in both compounds. For CeRuPO a pronounced decrease of rho(T) below 50K indicates the onset of coherent Kondo scattering which is confirmed by enhanced S(T). The temperature and magnetic field dependence of chi(T) and C(T) evidence ferromagnetic (FM) order at TC=15K. Thus, CeRuPO seems to be one of the rare example of a FM Kondo lattice. In contrast, CeOsPO shows antiferromagnetic order at TN=4.4K despite only minor changes in lattice parameters and electronic configuration. Additional 31P NMR results support these scenarios. LSDA+U calculations evidence a quasi two dimensional electronic band structure, reflecting a strong covalent bonding within the CeO and RuP layers and a weak ionic like bonding between the layers.