Two new experimental techniques have been developed and used to measure the differential Stark shifts between the Zeeman sublevels in excited atomic states. For states whose differential Stark shifts, in uniform electric fields attainable in the laboratory, are comparable to the hfs separation, the method of pure electricfield level crossing may be used. This method has been applied to the 6p 2 P 3 /2 state of rubidium and the lp 2 P 3 /2 state of cesium. The differential shifts are E(dbi)-JE(=fci)=0.521±0.021 Mc/(kV/cm) 2 in Rb, and 1.077±0.043 Mc/(kV/cm) 2 in Cs. For isotopes with no hyperfine structure (1 = 0) or states whose Stark shifts are small compared to their hfs, we have used the level-crossing technique with parallel electric and magnetic fields. This technique has been employed to measure the differential shifts in the 5s5p 3 Pi state of cadmium and the 6s6p 3 Pj state of mercury. The results are E(dbl) -E(0) = -2.550±0.105 kc/(kV/cm) 2 in Cd, and -2.355±0.090 kc/(kV/cm) 2 in Hg. The theory of quadratic Stark shifts in terms of scalar and tensor operators is presented, and the shifts in these four elements are calculated using the Coulomb approximation for the potential of the outer electron. The agreement between the experimental and the theoretical values is satisfactory.

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