Let R be a ring. An R -module M is called n -avoiding(co- n -avoiding) if for any set I with | I | = 1 + n and any family {N(i)}(i ? I) of submodules of M with ?N(i)=0(i ? I)(?N(i)=M(i ? I)), there is a finite subset J of I with | J | = n such that ?N(i)=0(i ? J)(?N(i)=M(i ? J)), and n is the smallest positive integer with this property. An R -module is then called avoiding(co-avoiding) if it is n-avoiding(co- n -avoiding) for some n ? 0. The definition of strongly n -avoiding(resp. co- n -avoiding) module is analogous, except that no restriction is placed on the cardinality of I . It is shown that avoiding modules are exactly finite uniform-dimensional modules and its dual respectively. We present examples showing that in the infinite case, they are different concepts from having infinite uniform dimension(resp. dual uniform dimension).