BEGIN {
   my $module =
      eval { require Module0; 'Module0' } ||
      eval { require Module1; 'Module1' } ||
      die("Module0 or Module1 are required\n");

   $module->import();
}
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You can pass arguments to import if you want to import specific symbols (like use Module qw( ... );) instead of the defaults (like use Module;), or you can omit the call entirely if you don't want to import anything (like use Module qw();).

Also, if you want $module to be available later on, you can move the my outside of the BEGIN.

my $module;
BEGIN {
   $module =
      eval { require Module0; 'Module0' } ||
      eval { require Module1; 'Module1' } ||
      die("Module0 or Module1 are required\n");

   $module->import();
}
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