A hose for refrigerant fluid or fuel oil service which comprises a core tube, a reinforcing layer and an outer cover, the core tube being of a composite structure having an inner plastic peripheral wall, an intermediate plastic peripheral wall and an outer rubbery peripheral wall. The inner and intermediate walls are formed of a selected class of polyamides and polyolefins, whereby the hose is rendered highly impermeable to fluid and moisture, greatly resistant to stress cracking and sufficiently flexible.