  Recent measurements of cosmic-ray spectra of several individual nuclear
species by the CREAM, TRACER, and ATIC experiments indicate a change in the
spectral index of the power laws at TeV energies. Possible explanations among
others include non linear diffusive shock acceleration of cosmic-rays,
different cosmic-ray propagation properties at higher and lower energies in the
Galaxy and the presence of nearby sources. In this paper, we show that if
supernova remnants are the main sources of cosmic rays in our Galaxy, the
effect of the nearby remnants can be responsible for the observed spectral
changes. Using a rigidity dependent escape of cosmic-rays from the supernova
remnants, we explain the apparent observed property that the hardening of the
helium spectrum occurs at relatively lower energies as compared to the protons
and also that the spectral hardening does not persist beyond $\sim (20-30)$ TeV
energies.
