For every polynomial we can define its coefficient of efficiency in distinguishing KLs: the number of different KLs that it can recognize as different, divided by the number of all really different KLs with a given number of crossings n. However, for nonalternating KLs, the exactness of the second number is impossible to prove by using polynomials: two really different KLs (e.g., mutant KLs) can have all existing polynomial invariants in common. This is more likely to happen then one might expect, because some polynomial invariants are only special cases of some more general invariants. For example, Alexander polynomials can be obtained from Conway polynomials or Jones polynomials. It seems that for every polynomial KL invariant it is possible to construct infinite classes of different KLs that this invariant is not able to distinguish. For example, all KLs obtained from a KL of the form p_{1},p_{2},...,p_{n} by any permutation of tangles p_{1}, p_{2}, ..., p_{n} cannot be distinguished by the Kauffman polynomial. An interesting class of KLs are those with trivial Alexander and Conway polynomials. We assume that every link with a trivial Alexander and Conway polynomial is a member of an infinite family of links, all having trivial Alexander and Conway polynomials. For n = 8 the 4component link 2,2,2,2 is a member of the family 2k,2k,2k,2k; for n = 9 the 3component link .(2,2) that has the nonminimal algebraic 10crossing representation (2,2),(2,2),2 is a member of the family (2k,2k),(2m,2m),2n with trivial Alexander and Conway polynomials. For n = 10: the 3component link (3,2 1) (2,2) is a member of the family (2k+1,2k 1) (2,2); the 3component link 3,2 1,2,2 is a member of the family 2k+1,2k 1,2,2; the 3component link 3,2,2 1,2 is a member of the family 2k+1,2,2k 1,2; the 4component link (2,2) 2 (2,2) that has the nonminimal 12crossing representation (2,2) 2 (2,2) is a member of the family (2,2) 2k (2,2); the 4component link .(2,2):2 that has the nonminimal 12crossing algebraic representation (2,2) 1,3,(2,2) is a member of the family (2,2) 1,2k+1,(2,2); the 4component link 103^{*}1.1.1.1::.1 that has the nonminimal 12crossing algebraic representation (2,2),2,2,(2,2) is a member of the family (2,2),2k,2k,(2,2) with trivial Alexander and Conway polynomials. Hence, for n £10 we succeeded to show that all links with trivial Alexander and Conway polynomials, except one, are members of the infinite families having the same property. The only exception is the link 2 0.2.2 0.2 0 for which we have not succeeded to find the corresponding family of links with trivial Alexander and Conway polynomials.
