  A quantum algebra $U_{p,q}(\zeta ,H,X_\pm )$ associated with a nonstandard
$R$-matrix with two deformation parameters$(p,q)$ is studied and, in
particular, its universal ${\cal R}$-matrix is derived using Reshetikhin's
method. Explicit construction of the $(p,q)$-dependent nonstandard $R$-matrix
is obtained through a coloured generalized boson realization of the universal
${\cal R}$-matrix of the standard $U_{p,q}(gl(2))$ corresponding to a
nongeneric case. General finite dimensional coloured representation of the
universal ${\cal R}$-matrix of $U_{p,q}(gl(2))$ is also derived. This
representation, in nongeneric cases, becomes a source for various
$(p,q)$-dependent nonstandard $R$-matrices. Superization of $U_{p,q}(\zeta ,
H,X_\pm )$ leads to the super-Hopf algebra $U_{p,q}(gl(1|1))$. A contraction
procedure then yields a $(p,q)$-deformed super-Heisenberg algebra
$U_{p,q}(sh(1))$ and its universal ${\cal R}$-matrix.
