The microwave spectra of the HCCS and DCCS radicals are studied in the frequency range of 160-400 GHz and the rotational transition series are assigned to several low-lying vibronic states in the CCS or H(D)CC bending vibration. Analysis is carried out to obtain effective constants for respective vibronic states. The gamma(eff) constants for the vibronic mu/kappa(2) Sigma states are found to be anomalous, in that the variation of the gamma(eff) constants in the same bending mode is large up to 3 GHz and the gamma(eff) value can reach to nearly twice the rotational constants B-v. This behavior cannot be understood by the current Renner-Teller theory. We have developed a theory to include cross vibronic interaction between two vibronic (2) Sigma(v(t)=1) states in different bending modes. Since the difference of the vibrational quantum numbers for these states is Delta(v(4)+v(5))=0, the interaction has a much larger effect than the one considered by Petelin and Kiselev [Int. J. Quantum Chem. 6, 701 (1972)] for the vibronic states with Delta(v(4)+v(5))=+/-2. Calculation with the newly derived expressions for gamma(eff) reproduces the anomaly in HCCS when the Renner parameters are fixed at epsilon(4)=-0.37 and epsilon(5)=+0.10 from the ab initio calculation, and the parameter epsilon(45) for the cross vibronic interaction is varied to be 0.4, a value which is obtained for the first time. The relative sign of the above epsilon(4) and epsilon(5) values is explicitly judged to be correct, In addition, the B-eff and the P-doubling constants in the (2) Pi(i) and (2) Delta(i) states are found to be effected by a higher-order perturbation of the cross vibronic interaction.