Given a hypergraph \(H=(X,E)\) denote by \(\tau\) (H) the minimum cardinality of a transversal set \(T\subset X\) and by \(\nu\) (H) the maximum number of pairwise disjoint edges of H. Ryser conjectured that \(\tau\) (H)\(\leq (r- 1)\nu (H)\) for each r-partite hypergraph H, which is strongly related to the Lovász conjecture: no partite hypergraph is (r-1)-fold \(\nu\)- stable. The author proves the conjecture for \(r=3\) and \(\nu\) (H)\(\leq 4\) and discuss some more general problems.