I did try what choroba suggested, and it didn't work.
I've put together three small files, for demonstration purposes:

Foo.pm

# Test module foo

package Foo;

use Bar;
#use Bar qw(BarFunc BarSub);

BEGIN {
    require Exporter;

    # set the version for version checking
    our $VERSION = 1.00;

    # Inherit from Exporter to export functions and variables
    our @ISA = qw(Exporter);

    # Functions and variables which are exported by default
    our @EXPORT = qw(FooFunc FooSub);

    # Functions and variables which can be optionally exported
    our @EXPORT_OK = qw();
}

sub FooFunc {
    return 'I am the FooFunc !';
}

sub FooSub {
    return 'FooSub reporting in !';
}

1;
[download]

Bar.pm

# Test module foo

package Bar;

use Foo;
#use Foo qw(FooFunc FooSub);

BEGIN {
    require Exporter;

    # set the version for version checking
    our $VERSION = 1.00;

    # Inherit from Exporter to export functions and variables
    our @ISA = qw(Exporter);

    # Functions and variables which are exported by default
    our @EXPORT = qw(BarFunc BarSub);

    # Functions and variables which can be optionally exported
    our @EXPORT_OK = qw();
}

sub BarFunc {
    return "I, BarFunc, solemnly declare: ".FooFunc()."\n";
}

sub BarSub {
    print "Howdy, Stranger !\n";
    print "I'm BarSub, and I'm going to tell you a secret: '".FooSub()
+."'\n";
}

1;
[download]

perlTest.pl

use Foo;
use Bar;

print FooFunc()."\n";

BarSub();
[download]

Now, when I run the command: perl perlTest.pl, I get the following output:

I am the FooFunc !
Howdy, Stranger !
Undefined subroutine &Bar::FooSub called at Bar.pm line 30.
[download]

Is the problem clearer now ?

EDIT:
Also, if I comment out the "use Foo;" and "use Bar;" lines from the modules, and uncomment the longer use lines (the ones with qw(...) on them), I get exactly the same output.