A variety $V$ is called {\it solid} if every identity 

in $V$ is satisfied as hyperidentity, i. e. 

if for every substitution of terms of $V$ of 

appropriate arity for the operation symbols 

in $s \approx t$, the resulting identity holds in $V$.

In the most cases it is very difficult 

to check whether an identity is satisfied 

as hyperidentity. The reason is that there are too much 

substitutions of terms for operation symbols. 

In this paper we will present methods 

to reduce the number of substitutions which are to check.

This will be done by using some equivalence relations 

on the set of all substitutions of terms 

for operation symbols. \par

Particular properties of the corresponding equivalence 

classes lead to the concepts of {\it strongly fluid} 

and {\it weakly unsolid} varieties.

The results will be applied to varieties of bands, 

of overcommutative semigroups and to some varieties 

of non-commutative groupoids.