We introduce classes of bilinear operators of \(\ell _{p,q}\) -type, i.e. classes of operators in which their sequences of s-numbers are in \(\ell _{p,q},\) and their properties and relationships are studied. We also introduce two classes of summing bilinear operators: the class \(\Pi _{p,q;r}^{ss}\) of strongly summing operators, and the class \(\Pi _{p,q;r,s}^{as}\) of absolutely summing operators. These classes share some properties with similar proofs. But, some others properties are specific for one or the other class. Also, they are somewhat more general than the multilinear summing classes introduced before by several authors. Relationships between classes of \(\ell _{p,q}\) -type and summing classes are given.
