I tried nasm as a linux assembler and I created a test file to see if it works.
My test.asm looks like this:

.model small
.stack 10
.data
mesaj db 'exemplu program$'
.code
start:
mov ax, @data
mov dx, ax
mov dx, offset mesaj
mov ah, 9
int 21h
mov ax, 4c00h
int 21h
end start

unfortunately, I received errors:

[ti@localhost Desktop]$ vi test.asm
[ti@localhost Desktop]$ nasm -o test -a test.asm
test.asm:1: error: attempt to define a local label before any non-local labels
test.asm:1: error: parser: instruction expected
test.asm:2: error: attempt to define a local label before any non-local labels
test.asm:2: error: parser: instruction expected
test.asm:3: error: attempt to define a local label before any non-local labels
test.asm:9: error: comma or end of line expected
test.asm:14: error: parser: instruction expected
[ti@localhost Desktop]$

How can I fix these errors?

Thanks!

I belive everything is incorrect.
1. You've chosen improper operating system for your code. The code is for DOS rather that for linux. 2. 'Int21' is DOS-specific.
3. There is no 'small' or 'large' models in linux since the CPU works in protected mode.
4. Same concerns registers which are named differently in this mode.
5. You used the syntax used by DOS assemblers which is usually non-acceptable by linux ones.

Assembler writing in Linux is much different than in DOS. Mainly because you can't write directly to hardware. But you still can do interesting things.
One thing that may be helpful. When learning Linux assembler, it's sometimes a good idea to see how your C prog looks in Asembler. It can be done using
gcc -S -O3 filename.c
It converts the C code to ASM code (it's not perfect, but with optimalization -O3 it's good).