Double-crystalline diblock copolymers of linear polyethylene (LPE) and hydrogenated polynorbornene (hPN) ire synthesized, and their crystallization is examined. LPE and hPN homopolymers are both highly crystalline, with similar melting points near 150 degrees C and chi(hPN/LPE) = 0.02. For symmetric diblocks, even when moderately segregated, crystallization of hPN breaks Out of the melt microdomains to create volume-filling spherulites. The LPE block subsequently crystallizes between the hPN crystallites, with the hPN and LPE crystal stems oriented orthogonally. At shallow Undercoolings, crystallization proceeds in two distinct steps, but at deeper undercoolings, only a single process is observed, following the temperature dependence of hPN crystallization. At these deeper undercoolings, crystallization of hPN initiates LPE crystallization so that the two processes are nearly simultaneous. By changing the block ratio, the crystallization behavior can be broadly tuned: in hPN-rich diblocks, the two crystallization processes are well-separated at any temperature, while in LPE-rich diblocks, the LPE block crystallizes first.