We have investigated the effect of nanometric grain size on magnetic properties of La0.7Ca0.3MnO3 nanoparticles having average particle size (Φ) of ∼17 nm. Temperature dependence of field-cooled (FC) and zero-FC (ZFC) dc magnetization indicate the existence of two different types of relaxation processes: a relatively high temperature regime where there is a broad maximum of the ZFC curve at T=Tmax (≫40 K) and another is a relatively low temperature regime that is characterized by a sharp maximum at T=TS (≈40 K). We believe that the broad maximum at Tmax is associated with the blocking of core particle moments, whereas the sharp maximum at TS is related to the freezing of surface spins. Waiting time (tw) dependence of ZFC relaxation measurements at T=50 K show weak dependence of relaxation rate [S(t)] on tw and dM/d ln(t) following a logarithmic variation in time. These features strongly support superparamagnetic (SPM) blocking of core particle moments at Tmax. At T=20 K, S(t) attains a maximum at tw=1000 s that establishes freezing phenomenon occurring at TS. The combination of topological disorder and magnetic phase separation may result in a magnetically disordered state at the grain surface. This, in tu- rn, results in magnetically uncoupled assembly of nanoparticles that eventually exhibits SPM blocking. The glassy behavior at TS has been attributed to the competing magnetic interactions stabilizing a spin-glass-like frozen state at the surface region of the nanometric grains.