Context :

Aims : This paper addresses the global molecular gas properties of a representative sample of galaxies hosting low-luminosity quasistellar objects .
An abundant supply of gas is necessary to fuel both the active galactic nucleus and any circum-nuclear starburst activity of QSOs .
The connection between ultraluminous infrared galaxies and the host properties of QSOs is still subject to a controversial debate .
Nearby low-luminosity QSOs are ideally suited to study the properties of their host galaxies because of their higher frequency of occurrence compared to high-luminosity QSOs in the same comoving volume and because of their small cosmological distance .

Methods : We selected a sample of nearby low-luminosity QSO host galaxies that is free of infrared excess biases .
All objects are drawn from the Hamburg-ESO survey for bright UV-excess QSOs , have \delta > -30 ^ { \circ } and redshifts that do not exceed z=0.06 .
The IRAM 30m telescope was used to measure the \@element [ ] [ 12 ] [ ] [ ] { \mathrm { CO } } ( 1 - 0 ) and \@element [ ] [ 12 ] [ ] [ ] { \mathrm { CO } } ( 2 - 1 ) transition in parallel .

Results:27 out of 39 galaxies in the sample have been detected .
The molecular gas masses of the detected sources range from 0.4 \cdot 10 ^ { 9 } M _ { \odot } to 9.7 \cdot 10 ^ { 9 } M _ { \odot } .
The upper limits of the non-detected sources correspond to molecular gas masses between \bf 0.3 \cdot 10 ^ { 9 } M _ { \odot } and \bf 1.2 \cdot 10 ^ { 9 } M _ { \odot } .
We can confirm that the majority of galaxies hosting low-luminosity QSOs are rich in molecular gas .
The properties of galaxies hosting brighter type I AGN and circumnuclear starformation regions differ from the properties of galaxies with fainter central regions .
The overall supply of molecular gas and the spread of the linewidth distribution is larger .
When comparing the far-infrared with the CO luminosities , the distribution can be separated into two different power-laws : one describing the lower activity Seyfert I population and the second describing the luminous QSO population .
The separation in the L _ { FIR } / L ^ { \prime } _ { CO } behaviour may be explainable with differing degrees of compactness of the emission regions .
We provide a simple model to describe the two power-laws .
The sample studied in this paper is located in a transition region between the two populations .

Conclusions :