We present a new optical biosensing technique based on registration of bounded optical surface waves (SWs) propagating along an external interface of a one-dimensional photonic crystal (1D PC). Unique tunable properties of 1D PCs permit the design of a 1D PC structure with one of surface modes abutting on the angle of the total internal reflection (TIR). This mode (p-polarized), in which the exited angle is infinitesimally close to the angle of TIR from the external medium, has a very large penetration depth in this medium (e.g., water) and may be used as a reference of bulk refractive index (RI) fluctuations. While another mode (s-polarized) is adlayer-thickness-sensitive one and less sensitive to bulk RI changes. This permits us to segregate the volume and the surface signals from the analyte and increase the sensitivity of the PC SW biosensor. The exploitation of the 1D PCs as substrates supporting the long-range surface wave propagation permits: (1) to increase the sensitivity of PC SW biosensors to the level� da~2x10-13m/Hz1/2 (that corresponds to mass sensitivity ma~0.2pg/mm2), (2) to segregate surface and volume events in biosensing (that may be an important advantage in applications where temperature and composition of the liquid under study vary over a wide range), (3) to enhance the detection of RI variation in the Abbe-like refractometer to the level ~8x10-8 RIU/Hz1/2.