The hyperfine structure of several highly excited 'D states in Rb and 'Cs has been measured. The D-state atoms were produced in a two-step — excitation process. In the first step, multiple scattering of the strong alkali-metal D & and D, lines from an rf lamp was used to excite atoms into the first excit- ed 'P levels. The intense tunable radiation from a cw dye laser was used in the second step to trans- fer P-state atoms into highly excited D states. Level-crossing and optical-double-resonance techniques were used for the determination of the absolute values of the hyperfine-interaction constants. The fol- lowing results (in MHz) were obtained for the magnetic dipole and the electric quadrupole interaction constants a and b: For Rb, I a(6 D2)I = 7.84(5), I b(6 D3,QI = 0.53(6) (bio & 0), a(6'D~, 2)I = 3.6(7), Ia(7' D,)I = 4.53(3), I b(7'D», ) I = 0.26(4) (bia & 0), Ia(7'D,)I = 2.2(5). For 'Cs, Iu(8'Du2) I = 98(8) Iu(8'Dsi2)l = o9(4). Iu(9'D3t2)l = 237(3) In(9'Dsi2)l = 05(2) Iu(10'D3i~)i = 1.52(3), I a(10'D , ) I = 0.4(2). The a factors generally deviate strongly from the values expected in a one-electron picture of the alkali-metal atom indicating the importance of polarization and correlation effects for these states. For Rb a comparison with a recent calculation including polarization effects is made. The b factors for Rb are the first significant values allowing a calculation of an alkali-metal- atom nuclear quadrupole moment from non-P-state data.