Cobordism invariants have been applied to both real and complex categories. For example, the index of 4k-dimensional manifolds was treated by Hirzebruch for the generalization of the Riemann-Roch theorem [3]. He also considered, in relation with this, virtual genus or virtual characteristics. But many invariants, such as virtual characteristics, have their origin in complex analytic category. In view of this, we consider certain complex analytic cobordism, i.e., quasilinear cobordism among quasilinear subvarieties in complex manifolds (see for the definition of quasilinear structure [4].) Quasilinear body has very simple type of singularities, as well as its quasilinear boundaries. Therefore, the theory of quasilinear cobordism can be reduced, through σ-processes, to that of non-singular cobordism theory.