Retro-ene type [2π + 2π + 2σ] and [3,3]-sigmatropic shift reactions involving the substituent groups R in heteroatom-substituted cyanates and thiocyanates RX-YCN and the isomeric isocyanates and isothiocyanates of the type RX-NCY (X = CR(2), NR', O, or S; Y = O or S) have been investigated computationally at the B3LYP/6-311++G(d,p) level. Retro-ene reactions of alkyl derivatives of the title compounds afford alkenes, imines, carbonyl and thiocarbonyl compounds together with HNCO (HNCS) or HOCN (HSCN). [3,3]-Sigmatropic shifts (hetero-Cope rearrangements) of the corresponding allyl, propargyl, benzyl, and aryl derivatives causes allylic rearrangements, propargyl-allenyl rearrangement, conversion of benzyl cyanates to o-isocyanatotoluenes, and conversion of N-cyanatoarylamines to o-isocyanatoanilines, etc. The corresponding rearrangements of allyl thiocyanates, arylamino thiocyanates and isothiocyanates, and arylsulfenyl thiocyanates and isothiocyanates are also described.