  We report large magnetoresistance (MR) at low temperatures in
single-crystalline nonmagnetic compounds TaAs$_2$ and NbAs$_2$. Both compounds
exhibit parabolic-field-dependent MR larger than $5\times10^3$ in a magnetic
field of 9 Tesla at 2 K. The MR starts to deviate from parabolic dependence
above 10 T and intends to be saturated in 45 T for TaAs$_2$ at 4.2 K. The Hall
resistance measurements and band structural calculations reveal their
compensated semimetal characteristics. The large MR at low temperatures is
ascribed to a resonance effect of the balanced electrons and holes with large
mobilities. We also discuss the relation of the MR and samples' quality for
TaAs$_2$ and other semimetals. We found that the magnitudes of MR are strongly
dependent on the samples' quality for different compounds.
