Spontaneous rotational-symmetry breaking in the superconducting state of the doped topological insulator Bi2Se3 has attracted significant attention as a candidate for topological superconductivity. We have studied the normal and the superconducting state of NbxBi2Se3 and SrxBi2Se3 using magnetoresistance, magnetization, penetration depth and specific heat. While no sign of a symmetry breaking of the three-fold in plane crystal symmetry is observed in the normal state, we find a clear two-fold in plane symmetry of the upper critical field in the superconducting state. This large basal-plane anisotropy of Hc2 (Γ=3.5) is attributed to two-component gap structure η = (η1, η2). A quantitative analysis of our data excludes more conventional sources of this twofold anisotropy and gives clear evidence for nematic superconductivity and some indications for topological superconductivity in both NbxBi2Se3 and SrxBi2Se3.