New complexes of formulae [Cu(HL(2))(H(2)O)(NO(3))](NO(3)) (1), [{Cu(L(1))(tfa)}(2)] (2), [{Cu(L(1))}(2)(pz)](ClO(4))(2) (3) and {[{Cu(L(1))}(2)(dca)](ClO(4))}(n) (4), where HL(1)=pyridine-2-carbaldehyde thiosemicarbazone, HL(2)=pyridine-2-carbaldehyde 4N-methylthiosemicarbazone, Htfa=trifluoroacetic acid (CF(3)COOH), pz=pyrazine (C(4)H(4)N(2)) and dca=dicyanamide [N(CN)(2)](-), have been synthesized and characterized. The crystal structures of these compounds are built up of monomers (1), dinuclear entities with the metal centers bridged through the non-thiosemicarbazone coligand (2 and 3) and 1D chains of dimers (4). In all the cases, square-pyramidal copper(II) ions are present, except for the square-planar ones in 3. Magnetic measurements show antiferromagnetic couplings in 2, 3 and 4. The susceptibility data were fitted by the Bleaney-Bowers' equation for copper(II) dimers derived from H=-2JS(1)S(2) being the obtained J/k values -4.8, -4.3 and -5.1K for compounds 2-4, respectively. The magnetic susceptibility of the already known [{Cu(HL(1))(tfa)}(2)](tfa)(2) compound has been also measured for the first time. The J/k value is -0.3K, lower than that in 2. The nuclease activity of 3 and 4 has been analyzed.