Abstract: For threaded connections for oil and gas applications using tubular goods of composite materials, substantially greater make up torque can be applied, with significantly improved tensile and sealing properties, by incorporating stress-relieving conical gradient sections adjacent each end of the threaded section of the composite member. Joining each of two composite tubular members to a single double ended male member having complementary surfaces, circumferential distortion is not concentrated at the end regions of the threaded sections but is distributed, relieving stresses and allowing increased makeup torque to be applied, greatly expanding the useful parameters of fiber reinforced tubular products.