We consider the real cubic system of differential equations ()()(),1,;,/,,/===QPGCDyxQdtdyyxPdtdx (1) ()(){}.3deg,degmax=QP A straight line ,0=++γβαyx ,,,C∈γβα )0,0(),(≠βα is invariant for (1) if there exists a polynomial ()yxK, such that the identity ()()()()yxKyxyxQyxP,,,γβαβα++≡+ holds. In this paper we show that if the cubic system admits an affine straight line of multiplicity two, then the line at infinity cannot have multiplicity greater than five. Theorem. Any cubic system having two invariant straight lines (including the line at infinity) of the multiplicity )5;2(m via affine transformation and time rescaling can be brought to the form .0,,23≠+++==bybxaxxyxx&& (2) For (2) 0=x is invariant straight line of multiplicity 21=m and the line at infinity has multiplicity 52=m. The perturbed cubic system 9/))4129)(3()69)(23()23)(((,9/)23)(23(22222222232εεεεεεεεεεεεεεεεεababayxyxbaaaxybyayxbxaxybxabxaxx−+−++++−++++++++++=++−+=&& (3) has six distinct invariant straight lines: ,23,21εεεbxalyxl−+=+= yyxababaxaxbaaallxlbxal)2)(4129()23()223)(23)(1(,,2322222226543εεεεεεεεεεεεεε+−+−+++++++++=⋅=++=2 which converge to 0=x when .0