For all families the variance of the response will depend on the mean and
will have the scale parameter as a multiplier. The form of dependence of
the variance on the mean is a characteristic of the response distribution;
for example for the poisson distribution the 
.
For quasi-likelihood estimation and inference the precise response distribution is not specified, but rather only a link function and the form of the variance function as it depends on the mean. Since quasi-likelihood estimation uses formally identical techniques to those for the gaussian distribution, this family provides a way of fitting gaussian models with non-standard link functions or variance functions, incidently.
For example, consider fitting the non-linear regression
this may be written alternatively as
where 
, 
, 
and
. Supposing a suitable data frame to be set up
we could fit this non-linear regression as
nlfit <- glm(y ~ x1+x2-1,family=quasi(link=inverse,variance=constant),
data=biochem)
The reader is referred to the manual and the help document for further information, as needed.