We have performed low-temperature specific heat $C$ and thermal conductivity $kappa$ measurements on the Ni-pnictide superconductors BaNi$_2$As$_2$ ($T_mathrm{c}$=0.7 K and SrNi$_2$P$_2$ ($T_mathrm{c}$=1.4 K). The temperature dependences $C(T)$ and $kappa(T)$ of the two compounds are similar to the results of a number of s-wave superconductors. Furthermore, the concave field responses of the residual $kappa$ for BaNi$_2$As$_2$ rules out the presence of nodes on the Fermi surfaces. We postulate that fully gapped superconductivity could be universal for Ni-pnictide superconductors. Specific heat data on Ba$_{0.6}$La$_{0.4}$Ni$_2$As$_2$ shows a mild suppression of $T_mathrm{c}$ and $H_mathrm{c2}$ relative to BaNi$_2$As$_2$.
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