Detections of CO, CS, SO, C
2H, HCO
+, HCN, HNC, H
2CO, and C
3H
2 are reported from LIRS 36, a star-forming region in the Small Magellanic Cloud. C
18O, NO, CH
3OH, and most notably CN have not been detected, while the rare isotopes
13CO and, tentatively, C
34S are seen. This is so far the most extensive molecular multiline study of an interstellar medium with a heavy element depletion exceeding a factor of four. The X = N(H
2)/I
CO conversion factor is ≃4.8x10
21cm
–2(K.km/s)
–1, slightly larger than the local Galactic disk value. The CO (1-0) beam averaged column density then becomes N(H
2)≃3.7x10
21cm
–2 and the density n(H
2)≃100cm
–3. A comparison with X-values from Rubio et al. (
1993A&A...271....9R) shows that on small scales (R≃10pc) X-values are more similar to Galactic disk values than previously anticipated, favoring a neutral interstellar medium of predominantly molecular nature in the cores. The I(
13CO)/I(C
18O) line intensity ratio indicates an underabundance of
12C
18O relative to
13C
16O w.r.t. Galactic clouds. I(HCO
+)/I(HCN) and I(HCN)/I(HNC) line intensity ratios are >1 and trace a warm (T
kin>10K) molecular gas exposed to a high ionizing flux. Detections of the CS J=2-1, 3-2, and 5-4 lines imply the presence of a high density core with n(H
2)=10
5-10
7cm
–3. In contrast to star-forming regions in the LMC, the CN 1-0 line is substantially weaker than the corresponding ground rotational transitions of HCN, HNC, and CS. CO, CS, HCO
+, and H
2CO fractional abundances are a factor ≃ 10 smaller than corresponding values in Galactic disk clouds. Fractional abundances of HCN, HNC, and likely CN are even two orders of magnitude below their `normal', Galactic disk values. The CN/CS abundance ratio is ≲1. Based on chemical model calculations, we suggest that this is because of the small metallicity of the SMC, which affects the destruction of CN but not CS, and because of the high molecular core density which also favors CN destruction.