We consider the real cubic di erential system x_ = P0 + P1(x; y) + P2(x; y) + P3(x; y)  P(x; y); y_ = Q0 + Q1(x; y) + Q2(x; y) + Q3(x; y)  Q(x; y); gcd(P;Q) = 1; (1) and the vector eld X = P(x; y) @ @x + Q(x; y) @ @y associated to system (1). A straight line l  x + y +  = 0, ; ;  2 C is invariant for (1) if there exists a polynomial Kl 2 C[x; y], deg(Kl)  2 such that the identity P(x; y) + Q(x; y)  ( x + y + )Kl(x; y); (x; y) 2 R2 (2) holds. The polynomial Kl(x; y) is called cofactor of the invariant straight line l. If m is the greatest natural number such that lm divides X(l) then we say that l has parallel multiplicity m: By present a great number of works have been dedicated to the investigation of polynomial di erential systems with invariant straight lines. The classi cation of all cubic systems with the maximum number of invariant straight lines, including the line at in nity, and taking into account their geometric multiplicities, is given in [1], [4], [5]. The cubic systems with exactly eight and exactly seven distinct ane invariant straight lines have been studied in [4], [5]; with invariant straight lines of total geometric (parallel) multiplicity eight (seven) - in [2], [3], [8], and with six real invariant straight lines along two (three) directions - in [6], [7]. In [9] it was shown that in the class of cubic di erential systems the maximal multiplicity of an ane real straight line is seven.