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After fixing a marking (V, W) of a quasifuchsian punctured torus group G, thecomplex length l_V and the complex twist tau_V,W parameters define aholomorphic embedding of the quasifuchsian space QF of punctured tori into C^2.It is called the complex Fenchel-Nielsen coordinates of QF. For a complexnumber c, let Q_gamma,c be the affine subspace of C^2 defined by the linearequation l_V=c. Then we can consider the linear slice L of QF by QF \capQ_gamma,c which is a holomorphic slice of QF. For any positive real value c, Lalways contains the so called Bers-Maskit slice BM_gamma,c. In this paper weshow that if c is sufficiently small, then L coincides with BM_gamma,c whereasL has other components besides BM_gamma,c when c is sufficiently large. We alsoobserve the scaling property of L.

Linear slices of the quasifuchsian space of punctured tori