Einstein-like equations with coupled-to-matter Lambda term

We consider Einstein-like gravitational equations with Lambda term proporti onal to the trace of the energy tensor. The possibility of Lagrangian formu lation is shortly discussed. The theory is consistent with the present-day observations, both at the local and cosmological level. Horizon-free cosmol ogical solutions are found and discussed. The initial condition S(0) = 0 (w here S(t) is the expansion factor and t the cosmic time) requires hyperboli c space.