Here we present an ultrasonic study on the elasticity of normal alkanes (n-heptane and n-nonane) in the nanopores of porous Vycor glass (average pore radius ). Above the melting temperature we have found a non-zero shear modulus for both n-heptane and n-nonane, which is also typical for the rotator phases of bulk alkanes at temperatures below the melting temperature. This points to the formation of a special molecular order of the adsorbed alkanes. Furthermore, the alkanes undergo a continuous stiffening over a broad temperature range (of for heptane or for nonane). The results clearly indicate that nanoconfinement induces an extremely broad continuous transition of heptane and nonane into a crystalline low-temperature phase.