We discuss the generalization of the Kerr-Schild (KS) formalism for general relativity and double field theory (DFT) to the heterotic DFT and supergravity. We first introduce a heterotic KS ansatz by introducing a pair of null O (d, d + G) generalized tangent vectors. The pair of null vectors are represented by a pair of d-dimensional vector fields, and one of the vector fields is not a null vector. This implies that the null property of the usual KS formalism, which plays a crucial role in linearizing the field equations, can be partially relaxed in a consistent way. We show that the equations of motion under the heterotic KS ansatz in a flat background can be reduced to linear equations. Using the heterotic KS equations, we establish the single and zeroth copy for heterotic supergravity and derive the Maxwell and Maxwell-scalar equations. This agrees with the KLT relation for heterotic string theory.1 O (1, d − 1) structure groups. It inherits from the left-right sector decomposition of the closed string, and each O (1, d − 1) group corresponds to the local Lorentz group of the target spacetime seen by the left and right sectors respectively. Since the double copy and KLT relations are also closely related to the left-right decomposition of the closed string, DFT provides a useful tool for describing such a hidden structure [38,39].The KS ansatz for pure DFT, which consists of the massless NS-NS sector only, is constructed in terms of a pair of null O (d, d) vectors [27]. The corresponding equations of motion can be reduced to linear equations by restricting the DFT dilaton appropriately. Based on this formalism, the classical double copy is extended to the entire massless NS-NS sector, and two independent Maxwell equations are derived from the KS equations. However, pure DFT itself cannot be a consistent low energy effective field theory of the string because of anomaly issues. Additional Yang-Mills gauge fields or Ramond-Ramond fields must be coupled to pure DFT to make a consistent theory.In the present paper, we extend the KS formalism for pure DFT to the heterotic DFT [40, 41] (see also [42] for the non-Riemannian origin). Heterotic DFT incorporates Yang-Mills gauge theory into pure DFT in a duality covariant manner, and it is described in terms of the O(d, d + G) gauged DFT, where G represents the dimension of the Yang-Mills gauge group 1 . The heterotic KS ansatz for the generalized metric is the same form as in the pure DFT case and written in terms of a pair of O (d, d + G) null vectors. However, its d-dimensional supergravity representations are quite different. One of the remarkable properties of the heterotic KS ansatz is that the null condition can be partially relaxed in the d-dimensional language while preserving the linearity of the field equations. We obtain the on-shell constraint for the O (d, d+ G) null vectors and DFT dilaton, which corresponds to the geodesic condition in the usual KS formalism in GR. Using the null and on-shell constraints together, the field equations under the heterotic...