Context : The tidal disruption of the Sagittarius dwarf Spheroidal galaxy ( Sgr dSph ) is producing the most prominent substructure in the Milky Way ( MW ) halo , the Sagittarius Stream .
Aside from field stars , it is suspected that the Sgr dSph has lost a number of globular clusters ( GC ) .
Many Galactic GC are thought to have originated in the Sgr dSph .
While for some candidates an origin in the Sgr dSph has been confirmed owing to chemical similarities , others exist whose chemical composition has never been investigated .

Aims : NGC 5053 and NGC 5634 are two of these scarcely studied Sgr dSph candidate-member clusters .
To characterize their composition we analyzed one giant star in NGC 5053 , and two in NGC 5634 .

Methods : We analyze high-resolution and signal-to-noise spectra by means of the MyGIsFOS code , determining atmospheric parameters and abundances for up to 21 species between O and Eu .
The abundances are compared with those of MW halo field stars , of unassociated MW halo globulars , and of the metal-poor Sgr dSph main body population .

Results : We derive a metallicity of [ Fe ii /H ] = -2.26 \pm 0.10 for NGC 5053 , and of [ Fe i /H ] = -1.99 \pm 0.075 and -1.97 \pm 0.076 for the two stars in NGC 5634 .
This makes NGC 5053 one of the most metal-poor globular clusters in the MW .
Both clusters display an \alpha enhancement similar to the one of the halo at comparable metallicity .
The two stars in NGC 5634 clearly display the Na-O anticorrelation widespread among MW globulars .
Most other abundances are in good agreement with standard MW halo trends .

Conclusions : The chemistry of the Sgr dSph main body populations is similar to that of the halo at low metallicity .
It is thus difficult to discriminate between an origin of NGC 5053 and NGC 5634 in the Sgr dSph , and one in the MW .
However , the abundances of these clusters do appear closer to that of Sgr dSph than of the halo , favoring an origin in the Sgr dSph system .