A loop (Q;
) is called a Basarab loop if the identities: (x
yx)(xz) = x
yz and (yx)
(xz
x) = yz
x hold. It is a special type of a G-loop. It was shown that a Basarab loop (Q;
) has the cross inverse property if and only if (Q;
) is an abelian group or all left (right) translations of (Q;
) are right (left) regular. In a Basarab loop, the following properties are equivalent: exibility property, right inverse property, left inverse property, inverse property, right alternative property, left alternative property and alternative property. The following were proved: a Basarab loop is a weak inverse property loop if it is exible such that the middle inner mapping is contained in a permutation group; a Basarab loop is an automorphic inverse property loop if a semi-commutative law is obeyed such that the middle inner mapping is contained in a permutation group; a Basarab loop is an anti-automorphic inverse property loop if every element has a two-sided inverse such that the middle inner mapping is contained in a permutation group; a Basarab loop is a semi-automorphic inverse property loop if the Basarab loop is exible, the middle inner mapping is contained in a permutation group such that a semi-cross inverse property holds; a Basarab loop with the m-inverse property such that a permutation condition is true is a cross inverse property loop if it is exible. Necessary and sucient conditions for a Basarab loop to be of exponent 2 or a centrum square were established.