Global bifurcation branches for boundary value problems of the type
are studied. Here denotes , is a bounded domain in , is a real parameter, the coefficients satisfy certain differentiability assumptions. It is shown that the set of nontrivial solutions generically consists of a finite or countable system of smooth, one-dimensional curves in , . Further, also generically, all eigenvalues of the linearized problem are simple, and the branches of nontrivial solutions bifurcating from these eigenvalues are smooth curves which either meet infinity or are closed loops which meet an even number of distinct eigenvalues. Some examples are given showing that both alternatives really can occur. (It is known from the Rabinowitz result that the second one is excluded in the case of ordinary differential equations).