Let \(\{f_ 1,...,f_ r\}\) be a family of contractions of a complete metric space X. A subset A of X is called invariant or self-similar if it satisfies \(A=f_ 1(A)\cup...\cup f_ r(A).\) It is known that this equation has a unique non-empty compact solution. This paper considers a generalisation called mixed invariant sets by the author. Given an \(r\times r\) matrix T\(=(t_{ij})\) of zeros and ones and a family \(\{f_ 1,...,f_ r\}\) of contractions, an r-tuple \((A_ 1,...,A_ r)\) of subsets of X is called mixed invariant if \[ A_ i=\cup_{\{j:t_{ij}=1\}}f_ i(A_ j),\quad i=1,...,r. \] Again it is not hard to show that this equation has a unique r-tuple \((A_ 1,...,A_ r)\) of non-empty compact sets as solution (the result remains true if one replaces the \(f_ i\) by contractions \(f_{ij})\). For other papers dealing (independently) with the same subject see e.g. M. F. Barnsley, J. H. Elton and D. P. Hardin [Constructive Approximation 5, No.1, 3-31 (1989; Zbl 0659.60045)] and R. D. Mauldin and S. C. Williams [Trans. Am. Math. Soc. 309, No.2, 811- 829 (1988; Zbl 0706.28007)]. The author treats the relationship with the recurrent sets introduced by the reviewer [see also T. Bedford, J. Lond. Math. Soc., II. Ser. 33, 89-100 (1986; Zbl 0606.28004)] and discusses the construction of mixed invariant sets. A final result states that if T is irreducible then each of the \(A_ i\) separately is self- similar, if one allows infinitely many contractions.